Game-Theoretic Approaches for Power-Generation Companies’ Decision-Making in the Emerging Green Certificate Market

Abstract

This study examines the decision-making optimization of Power-Generation Enterprises (PGEs) in the green certificate market, with a focus on balancing bidding strategies and carbon-reduction targets. Given the increasing complexity of the green certificate market, the research employs Bayesian games, evolutionary games, and Stackelberg games to systematically analyze the strategic behavior of PGEs and their interactions within the market framework. The findings demonstrate that game theory facilitates cost structure optimization and enhances adaptability to market dynamics under policy-driven incentives and penalties. Additionally, the study explores the integration of stochastic modeling and machine learning techniques to address market uncertainties. These results provide theoretical support for policymakers in designing efficient green electricity market regulations and offer strategic insights for PGEs aligning with carbon neutrality objectives. This work bridges theoretical modeling and practical application, contributing to the advancement of sustainable energy policies and the development of green electricity markets.

1. Introduction

During the initial stage of the new energy industry in China, a series of challenges were encountered, such as the mismatch between the development of renewable energy. Additionally, the early renewable energy industry was highly dependent on financial subsidies. As the renewable energy industry continued to grow, the demand for national financial subsidies also increased. According to the Ministry of Finance, by the end of 2017, the national renewable energy subsidy gap had reached 100 billion yuan. These issues prompted the Chinese government to seek market-oriented solutions to promote the consumption of renewable energy, alleviate financial subsidy pressures, and facilitate the transformation of the energy structure [1,2,3].

To address these issues, the Chinese government introduced the green certificate trading system. A green certificate is an electronic certificate issued by the state to power-generation companies for each megawatt-hour of non-hydro renewable energy electricity put onto the grid, with a unique identification code. The launch of green certificate trading aims to compensate for the insufficiency of financial subsidies through market mechanisms, reduce the reliance on direct national subsidies, and encourage renewable energy power-generation companies to continue investing and operating. Green certificate trading has become a key instrument to promote renewable energy consumption and support China’s dual carbon goals [4].

On 27 January 2024, the National Development and Reform Commission, the Ministry of Finance, and the National Energy Administration jointly issued the “Notice on Strengthening the Connection Between Green Electricity Certificates and Energy Conservation and Emission Reduction Policies to Vigorously Promote the Consumption of Non-Fossil Energy”. This further improved the issuance and trading system of green certificates, stimulating the potential demand for green certificates. With the introduction of the new green certificate policy, enterprises, as the main body of green certificate transactions, purchase green certificates through bilateral negotiations, listing transactions, and centralized bidding transactions in the green certificate market to fulfill the national policy requirements for increasing the proportion of green energy consumption [5].

The “Exploration and Practice Report on China’s Energy Regulation” demonstrates substantial advancements in the green transition of China’s energy and electricity production paradigms, facilitating the development of a renewable energy infrastructure and the realization of dual carbon objectives. For the year 2022, the new energy market transaction volume in China had reached 3.465 trillion kilowatt-hours, constituting 38.4% of the total new energy generation, marking a 14-percentage-point increase from the year 2020. Additionally, the scale of green electricity and green certificate transactions had been expanding steadily. By the end of October 2023, the cumulative green electricity transaction volume had escalated to 878 billion kilowatt-hours, with the issuance of 148 million green certificates [6].

In the future, as the national green electricity policy is promoted and the willingness of the whole society to consume green electricity increases [7], the scale of the green electricity market will further expand. However, with the increase of green certificate trading entities and the improvement of market liquidity, the complexity of market transactions will also increase, which may affect the efficiency and transaction costs of the green certificate trading system. In view of this, this study will focus on analyzing the development of the green certificate market and its specific impact on corporate bidding strategies, aiming to provide in-depth insights and strategic recommendations for policymakers and market participants [8].

To demonstrate the necessity of this survey and to ensure that the selected literature possesses high research value and academic quality, this study has chosen the Science Citation Index Expanded (SCI-EXPANDED) and Social Sciences Citation Index (SSCI) from the Web of Science, focusing on the most recent decade for data sources including authors, titles, source publications, and abstracts. When conducting literature searches in the field of green electricity, keywords included “renewable energy certificate”, “green power”, and “renewable energy”. In relation to the electricity market, the keywords selected were “strategy”, “bidding strategy”, and “electricity market”. After an initial search yielded a substantial number of documents, we filtered them based on relevance and academic merit, excluding duplicates and documents with low relevance. This selection process ensured the quality of the 12,026 documents ultimately chosen for academic research.

Using the VOSviewer bibliometric software (https://www.vosviewer.com/ (accessed on 21 December 2024)), six clusters were generated, as demonstrated in Figure 1. Cluster 1, themed “Green Electricity”, encompasses 16 keywords, focusing primarily on the utilization of renewable energy sources and their environmental benefits. Cluster 2 centers on “Electricity Markets” and “Power Systems”, comprising 13 keywords. Cluster 3, with “Energy Transition” at its core, includes 12 keywords. Both Cluster 4 and Cluster 6 consist of 10 keywords each, mainly addressing technical issues related to “Energy Engineering”, “Energy Storage”, and “Optimal Bidding Strategies”. Cluster 5 contains 11 keywords, emphasizing the significance of environmental policies and global development goals. From Figure 1, these clusters reveal the current academic community’s primary research focuses within the fields of energy and electricity markets.

Through visualization analysis of academic research, including keyword networks (Figure 1) and density mapping (Figure 2), it is evident that while there has been significant research on renewable energy and green electricity markets, studies focusing on the corporate-level impacts of the green certificate market—particularly on bidding strategies—are still in their infancy. For example, keywords such as “renewable energy” and “policy” dominate the research landscape, reflecting a strong governmental focus on green energy systems. However, the limited frequency of terms like “bidding strategy” or “corporate behavior” underscores the lack of attention to the strategic responses of enterprises in this context. This gap suggests a critical need for further investigation into how firms navigate the evolving green electricity market and adapt their strategies to meet policy-driven requirements.

To address this gap, this study investigates the behavioral decision-making of Power-Generation Enterprises (PGEs) in the green certificate market, with a particular focus on their bidding strategies. Game-theoretical methods—such as Bayesian, evolutionary, Stackelberg, and reinforcement learning-based game models—are applied to analyze how enterprises optimize their cost structures, bidding approaches, and compliance with policy mechanisms. By exploring these dynamics, this research provides in-depth insights for policymakers seeking to design efficient market regulations and for market participants aiming to enhance their competitiveness and operational sustainability.

The remaining sections of this paper are organized as follows: Section 2 provides a detailed investigation of the development status and processes of green certificate trading in China. Section 3 reviews five main game-theoretical methods applied in this context. Section 4 evaluates the impacts of green certificate trading on PGEs, including effects on cost structures and bidding strategies. Section 5 summarizes game-theoretic measures to enhance the competitiveness of PGEs, while Section 6 outlines policy recommendations and addresses future challenges. Finally, Section 7 concludes the survey with a summary of findings and implications. For ease of reference, a nomenclature is provided at the end of the paper.

2. New Green Certificate Market

Renewable energy generation, as a representative of clean energy, delivers significant environmental benefits and is referred to as “green power”. Power-Generation Enterprises produce green power using renewable energy sources and obtain Renewable Energy Certificates (RECs) through certification. With the release of the Notification, China’s green certificate system has been further optimized and refined, injecting new momentum into the promotion of renewable energy [9].

The Notification highlights the deep integration of green certificates with energy conservation and emission-reduction policies, specifying that non-fossil energy is excluded from total energy consumption and intensity control metrics. It also refines the accounting methods for incorporating electricity associated with green certificates into energy-saving evaluation indicators, promoting more efficient energy-conservation efforts at the regional level. Additionally, the Notification introduces diversified trading methods, strengthens the integration of green certificates with carbon markets, expands application scenarios, sets deduction caps for electricity linked to green certificates, and establishes standardized management rules [10]. These measures have significantly enhanced the market vitality and transparency of green certificate trading, increased its international recognition, and laid a solid foundation for the broader application of renewable energy and low-carbon development.

Against this backdrop, the New GC (GC) Market has further improved market rules and operational mechanisms, providing greater flexibility and efficiency for the integration and promotion of renewable energy. Compared to traditional green certificate trading mechanisms, the GC Market has made notable advancements in trading participants, pricing mechanisms, and international alignment. The scope of trading participants has expanded from Power-Generation Enterprises to include electricity consumers and intermediaries, effectively increasing market coverage and boosting demand for green certificates. In terms of pricing, the GC Market has introduced a dynamic pricing system that reflects real-time supply-demand relationships, ensuring more accurate market value representation while avoiding inefficiencies and market failures caused by fixed pricing models [11].

However, despite its progress, the GC Market faces several challenges. Regional imbalances in renewable energy generation and consumption result in an oversupply of green certificates in some areas and shortages in others [10,12]. Moreover, integrating technical standards, certification systems, and carbon markets on an international scale remains complex. These issues demand enhanced market management capabilities and greater policy coordination.

To address these challenges, the GC Market is actively implementing solutions. For instance, cross-regional green certificate trading and the application of energy-storage technologies can help optimize supply-demand distribution, improving the efficiency of green certificate utilization. Simultaneously, establishing unified international certification standards and connecting the GC Market with global carbon markets will not only enhance the international competitiveness of China’s green certificates but also provide a new model for global renewable energy collaboration. The advanced energy-storage technologies discussed in “Energy Storage Systems: A Comprehensive Guide” offer robust technical support for improving supply-demand balance and supporting dynamic pricing, ensuring the efficient operation of the GC Market [13].

Overall, the establishment of the GC Market has revitalized green certificate trading, yet its development remains influenced by policies, technologies, and market environments. From rule design to implementation, the promotion and application of green certificate trading are still in the process of continuous refinement. To fully understand its operational mechanisms and its role in advancing renewable energy development, it is essential to analyze its current development status and challenges in depth.

2.1. Development Status of Green Certificate Trading

Internationally, the green certificate market has seen early development, with many countries having established mature green certificate trading systems. In the United States, 30 states and the District of Columbia have implemented Renewable Portfolio Standards (RPS), with varying definitions for recognized green electricity.

The U.S. green electricity mandatory trading market is divided into mandatory and voluntary markets. The mandatory market requires electricity suppliers to ensure a certain proportion of their power comes from renewable sources within a specified time. Companies can meet these standards by self-producing or purchasing renewable energy certificates, or face penalties. Most states with carbon quota systems in the U.S. have established an REC trading system, which includes certification, trading, and regulatory mechanisms for renewable energy. The voluntary market is more diverse and flexible in supply channels and purchase methods, with eight main voluntary purchase methods currently on the market.

In recent years, as the cost of renewable energy generation has decreased, the price of green certificates has also significantly dropped, with a reduction of over 50% between 2014 and 2017, and has stabilized since 2018. As of June 2023, 29 states, the District of Columbia [14], and three overseas territories in the U.S. have implemented renewable energy quota systems, covering 58% of the U.S. electricity retail market. Of these, 12 states have mandated that their electricity suppliers must use renewable energy exclusively by 2050.

The green certificate market in Europe is more mature. The EU Renewable Energy Directive (Directive 2009/28/EC) defines the main functions of green certificates, requiring member states to establish national green certificate registries and manage them through the European Energy Certificate System (EECS) and the Association of Issuing Bodies (AIB), achieving full traceability of green certificates [15].

According to the EU Directive 2009/28/EC, all member states must establish national Guarantees of Origin (GO) registries, follow the unified EECS, and be managed by the AIB. Currently, 20 European countries comply with the EECS requirements and use the AIB system. The issuance, transfer, and withdrawal of each GO can be tracked through the registries of each country [16]. If electricity consumers purchase GOs as proof of using green electricity, the corresponding GOs will be canceled in the registry to prevent double counting. GOs must be traded or canceled within 12 months [17], or they will become invalid, here is a comparative overview of renewable energy certificate types across various regions, as summarized in Table 1.

During the period from January to September 2023, the green certificate trading market in China engaged 2382 enterprises, amassing a transaction volume of 10.88 billion kilowatt-hours, a fourfold increase compared to the corresponding period in the prior year. Specifically, the intra-provincial green electricity transactions constituted 8.12 billion kilowatt-hours, whereas the inter-regional green electricity transactions amounted to 2.76 billion kilowatt-hours. These data signify a notable advancement in the facilitation of renewable energy utilization and the marketization of energy transactions in China, thereby solidifying the groundwork for the attainment of sustainable, low-carbon energy development objectives.

2.2. China Green Certificate Trading Process

Since its inception in 2017, China’s GEC system has undergone a series of significant developments and policy evolutions. These changes have not only propelled the development of the green power market but also provided strong support for the marketization of renewable energy projects. An overview of the development timeline and policy evolution of China’s GEC system is illustrated in Figure 3.

• According to the “Notice”, released by the National Energy Administration on 25 July 2023, the main processes of green certificate trading in China include issuance, trading, and cancellation of green certificates. Each green certificate represents 1 megawatt-hour of renewable energy settlement electricity. The “newness” of the notice is primarily reflected in the following aspects:

• Exclusion of Non-Fossil Energy from Total Energy Consumption and Intensity Regulation: It is clarified that the consumption of non-fossil energy will be excluded from the total energy consumption and intensity control in the evaluation and assessment of energy-saving targets at the provincial level. This measure is designed to incentivize the use of non-fossil energy sources.

• Integration of Green Certificate Transaction Volume into Energy Conservation Assessment Indicators: Green certificates are positioned as the fundamental vouchers for renewable energy electricity consumption, promoting their application in energy conservation evaluation and assessment processes.

• Specification of Green Certificate Transaction Volume Deduction Methods: The notice establishes detailed policies for the deduction of green certificate transaction volumes to ensure accurate accounting of renewable energy consumption.

• Acceleration of Record-Filing and Issuance of Green Certificates for Renewable Energy Projects: There is a requirement to expedite the issuance of green certificates and to enhance the proportion of record-filed renewable energy power-generation projects.

• Expansion of the Scope of Green Certificate Transactions: The notice encourages meeting renewable energy consumption needs through green certificate transactions and supports various enterprises in achieving green and low-carbon development by purchasing green certificates.

• Standardization of Green Certificate Trading System: Green certificate trading is to be conducted through platforms such as the China Green Electricity Certificate Trading Platform, standardizing the trading processes and systems.

• Expansion of Green Certificate Application Scenarios: The notice promotes the application of green certificates in areas such as green electricity consumption certification, energy conservation and carbon management, carbon accounting, and carbon market management.

• Strengthening of Organizational Implementation: The notice calls for enhanced coordination and supervision in the implementation of the green certificate system to ensure the effective execution of the policy.

Currently, China’s green certificate issuance and trading system issues certificates monthly based on data provided by power grid enterprises and electricity trading institutions, achieving a closed-loop management of the entire issuance and trading process through real-name green certificate accounts, ensuring the accuracy and reliability of the issuance work. For conventional hydropower stations, tradable green certificates are not issued; the corresponding certificates are transferred without compensation along with the electricity transactions, while tradable green certificates are transferred through market transactions for compensation.

Trading takes place on the China Green Electricity Certificate Voluntary Subscription Platform, allowing registered government agencies, enterprises, institutions, and individuals to subscribe to or sell green certificates. During the transaction, each green certificate can only be sold once within its validity period, and the corresponding electricity no longer enjoys national subsidies. All transaction records are filed for inquiry by regulatory authorities and market participants, and the entire process is under strict supervision and management by relevant national departments, ensuring fairness and transparency.

3. Game-Theoretical Methods

Currently, several methods are employed to study green certificate markets. Econometric models are frequently used to analyze historical data and predict market trends, focusing on relationships between variables such as prices, demand, and policy impacts. Optimization algorithms effectively address single-objective problems, such as cost minimization or renewable energy adoption maximization, within predefined constraints. Simulation-based approaches, including agent-based modeling, are also applied to replicate market dynamics and policy outcomes under different scenarios. However, these methods often fail to adequately capture the strategic and interactive behaviors of market participants in complex environments, such as green certificate markets.

In contrast, game theory provides a robust framework to analyze decision-making processes involving multiple stakeholders, each with conflicting or cooperative objectives. Unlike econometric models that are descriptive or optimization algorithms that assume static environments, game theory is inherently dynamic and accounts for the strategic interactions among participants. This makes it particularly relevant for green certificate markets, where actions taken by one party—such as bidding strategies or policy responses—directly influence others. Moreover, game theory allows for modeling reward-punishment mechanisms, competition for limited resources, and coalition formation [18,19].

Game theory, a mathematical theory that studies decision-making problems, provides an optimization method for Power-Generation Enterprises in green certificate trading for their bidding strategies. With the introduction of new green certificate policies, the market has become more stringent in its requirements for carbon emission management and has set higher targets for the proportion of renewable energy, presenting new challenges to the green certificate trading market. Against this backdrop, the importance of game theory in modern power systems is increasing, especially in decision optimization and strategy formulation in key areas such as green electricity trading, green certificate markets, and carbon markets.

By applying game-theoretical methods, researchers can better understand the strategic decision-making processes in green certificate markets, predict equilibrium outcomes, and design incentive mechanisms that align individual behaviors with broader sustainability goals. To illustrate the application of game theory in energy market strategies, Table 2 summarizes several core concepts of game theory.

3.1. Bayesian Game-Theoretical Method

Bayesian games, as a type of static game with complete information, are used to analyze the interactions between participants. In these types of games, participants are assumed to be completely rational and to possess the same and complete information. Before the game begins, participants have a full understanding of the game’s rules, possible actions, and the strategies of other players, with their strategy sets and payoff functions being fixed and unchanging. After the game starts, each participant simultaneously chooses their strategy with the aim of maximizing their own benefit. When no participant can improve their own benefit by changing their strategy, the game reaches an equilibrium state, a typical example of which is the Nash equilibrium [20].

Bayesian game theory applications in electricity trading primarily focus on simulating strategic decision-making under uncertainty to address issues related to market efficiency, pricing strategies, energy management, and demand response. These studies often necessitate accurate data forecasting and sophisticated computational methods to ensure the efficacy and practicality of the models. By employing Bayesian games, it is possible to anticipate and refine trading strategies within the electricity market, thereby enhancing market efficiency and participant revenues. Table 3 provides an overview of relevant research and how Bayesian games have been utilized to tackle specific problems.

Table 3

A Summary of Bayesian game theory applications in electricity and green certificate markets.

Paper	Players	Game Description	Advantages	Limitations
[21]	Strategic agents with asymmetric information	Stochastic dynamic games with asymmetric information, focusing on common information and signaling	Introduces CIB-PBE and sequential decomposition for computation	Complex computation due to signaling and asymmetric information
[22]	User and smart jammer	Hierarchical interaction model with incomplete information, focusing on anti-jamming strategies	Derives Stackelberg equilibrium and proves existence/uniqueness	Assumes perfect channel state information for the user
[23]	Residential communities with PEVs	Bayesian game for energy consumption scheduling with incomplete information on charging costs and discharging profits	Proves existence of Bayesian Nash equilibrium and proposes iterative algorithm	Assumes communities have different service charges with known distributions
[24]	IDS and attackers in VANETs	Self-adaptive IDS that uses Bayesian game theory and deep reinforcement learning for dynamic intrusion detection	Improves detection rate and reduces detection time/overhead	Requires significant computational resources for DQN training
[25]	Electric vehicles in residential microgrids	Bayesian game for V2V energy trading considering network constraints and uncertainties	Improves revenue for EVs and reduces energy loss	Assumes perfect information on network constraints and DERs
[26]	Multiple utility companies in a smart grid	Bayesian game for noncooperative pricing where companies have private information about substitution elasticity	Allows for incomplete information scenarios, uses fictitious play algorithm to find Bayesian Nash equilibrium	Assumes companies can estimate private parameters of competitors
[27]	Agents in a network of dynamical systems with uncertain objectives	Bayesian graphical games to model situations where agents are uncertain about their payoff functions and must use observed evidence to update beliefs	Establishes relationship between beliefs and distributed control policy, proposes belief update methodologies	Requires agents to have some knowledge of the game structure and other agents’ behavior

Based on this, the payoff function for the i-th participant in the green certificate market can be described as:

(1)$U_{\mathrm{bayes}-\mathrm{game}}^i=U_i(s_1,s_2,\cdots ,s_n)$

In the green certificate market, the goal of each participant is to maximize their own payoff, which may include economic returns from trading green certificates, cost savings from meeting compliance requirements, or avoiding penalties. Therefore, each participant needs to solve the following optimization problem:

(2)$\max U_i(s_1,s_2,\dots ,s_n) s_i\in S_i$

where S_−i represents the strategies of all participants except participant i. When the game reaches equilibrium, the expected payoffs of all participants must satisfy the following inequality:

(3)$u_i({s^{*}}_i, {s^{*}}_{-i})\ge u_i(s_i, {s^{*}}_{-i}) \forall s_i\in S_i$

In the green certificate market, game models must consider practical factors such as market uncertainty, policy constraints, and the volatility of green certificate prices. While traditional game models theoretically provide a clear decision-analysis framework for participants, they face significant limitations in real-world applications. First, decision-making in the green certificate market is often influenced by bounded rationality, such as inaccurate predictions of future certificate prices. Second, market information is not fully transparent, and certain participants may have superior knowledge of policy adjustments or market changes. Additionally, the dynamic nature of the green certificate market evolves over time, making static game models insufficient to fully capture market behavior.

To better reflect the realities of the green certificate market, more flexible and adaptive game models, such as evolutionary game models or dynamic game models based on deep reinforcement learning, can be introduced. These models are better equipped to capture the long-term dynamic adjustments of market participants and describe the evolution of the market under complex policy constraints and uncertainties, thereby providing more comprehensive support for policy design and market optimization.

3.2. Evolutionary Game-Theoretical Method

Evolutionary Game Theory (EGT) originates from the theory of biological evolution and was first proposed by John Maynard Smith in 1973 [28]. Compared to classical game theory, EGT takes into account the time of evolution and the dynamic changes in strategies, emphasizing the non-perfect rational behavior of participants and the strategy-selection mechanism based on genetics [29,30]. Several key concepts in EGT include Evolutionarily Stable Strategy (ESS), Replicator Dynamics (RD), and Multi-population Evolutionary Stabilization Strategy (MESS). Figure 4 depicts the typical algorithmic process of a long-term evolutionary game.

Evolutionary Game Theory methods simulate the strategic choices and behavioral evolution of market participants in the dynamically changing market environment, addressing strategic interaction issues among different entities such as Power-Generation Enterprises, electricity-purchasing enterprises, consumers, and governments. These studies often incorporate computational models and algorithms to predict and optimize market strategies, thereby enhancing market efficiency and participant revenues. The application of evolutionary games in electricity and green certificate trading is summarized in Table 4.

Within the framework of ESS and MESS, a system dynamics model is introduced to simulate the dynamic evolution process of the GC market. The focus lies on understanding the price-formation mechanisms, behavioral responses to policy incentives, and the dynamic balance of supply and demand within the GC market.

In the ESS context, it is assumed that there are n populations, and within the population, there is a pure strategy s and $s^{\prime }\in S$. The mutant population’s strategy is $\epsilon s^{\prime }+(1-\epsilon )s$, where ${\epsilon }^{\prime }\in (0, 1)$, and there always exists an $\epsilon \in (0, {\epsilon }^{\prime })$, such that the following inequality is satisfied, where U is the payoff function described as

(4)$U(s, \epsilon s^{\prime }+(1-\epsilon )s)>U((s^{\prime },\epsilon s^{\prime }+(1-\epsilon )s)$

Then, the evolutionary game reaches the ESS state. For MESS, it is assumed that there are n populations, with strategy combinations X = {X₁, X₂, …, X_n} ∈ Y and Y = {Y₁, Y₂, …, Y_n} ∈ Y, where Y is not equal to X and is within the strategy space [31]. When $\exists 0<\omega <1$, $\forall 0<\sigma <\omega$, and $\forall M=\sigma Y+(1-\omega )X$ (where $\forall M\ne X, \forall M\ne Y$) satisfies the expected payoff as

(5)$U(X_i, X_{-i})>U(Y_i, X_{-i}) i=1,2,\cdots ,n$

Based on (5), it can be seen that if the pure strategy $X_i$ is a MESS, it must be a strictly refined Nash equilibrium strategy, and its evolutionarily stable equilibrium must also be a Nash equilibrium. In fact, the evolutionarily stable equilibrium is a refinement of the Nash equilibrium, but weakly dominated Nash equilibrium strategies are not necessarily MESS [30,32]. Thus, MESS is a concept of equilibrium that can describe the general characteristics of evolutionary games, which is much more complex than Nash equilibrium Obviously, when the evolutionary game reaches an MESS state, in which the remaining individuals will tend to adopt the strategy combination X_−i ($X_{-i}\in M, \forall X_{-i}\ne X$).

Building on this foundation, the system dynamics model further extends the analysis of market participants’ behavior and the price evolution within the GC market. The key market participants include renewable energy producers, traditional energy producers, electricity consumers, and government regulatory agencies. Renewable energy producers enter the market by generating GCs, while consumers fulfill their compliance obligations by purchasing GCs according to quota policies. The government regulates the market through instruments such as subsidies, carbon taxes, and penalties. The primary input variables of the system dynamics model include:

• Price factors: Electricity price, carbon price, and green certificate price;

• Policy incentives: Government subsidies, carbon taxes, and GC quotas;

• Supply-demand dynamics: GC supply and demand;

• Behavioral variables: Production costs and market response speed.

The core assumptions of the model include: the green certificate price is dynamically adjusted by the balance of market supply and demand; enterprises adjust their strategies based on the principle of profit maximization; and government policies drive market behavior evolution by reducing production costs through subsidies and limiting carbon emissions through carbon taxes. On this basis, the system’s expected payoffs and replicator dynamic equations are constructed to further analyze the evolution path of green certificate prices, behavioral adjustments of market participants, and the impact of policy incentives on supply-demand equilibrium.

Replicator dynamics is a very important concept defined in Evolutionary Game Theory. The concept of replicator dynamics is generally adopted to describe the speed of response to strategy selection adjustment, revealing the evolutionary law of population numbers or proportions [33]. Replicator dynamics equation can be described by a dynamic differential equation for the probability or frequency (denoted by x_i) of a particular pure strategy X_i being adopted in a population. Based on this, a replicator dynamics equation can be expressed as $\mathrm{d}{x}_i/\mathrm{d}t=x_i[E(X_i)-E_{\mathrm{av}}(X_i)]$, which shows that $\mathrm{d}{x}_i/\mathrm{d}t$ is directly proportional to the number or proportion of groups choosing the strategy X_i, i.e., x_i, and is also directly proportional to the difference between the expected gain E(X_i) and population average gain E_av(X_i). As explained by [30], if we assume that $\theta , {\theta }^{\ast }\in \Omega$ are mixed strategies in an evolutionary game, where ${\theta }^{\ast }$ is a MESS and if ${\theta }^{\ast }$ satisfies the following two conditions: (a) the equilibrium condition, (E(θ, θ*) ≤ E(θ*, θ*), ∀θ ∈ Ω), and (b) the stabilization condition, if E(θ, θ*) = E(θ*, θ*), and then for ∀θ ≠ θ*, there is E(θ, θ) < E(θ*, θ), then the group state p* = θ* is defined as an asymptotically stable equilibrium point for the replicator dynamics equation model. In this model, the replicator dynamic equation serves to analyze how market participants converge to a long-term evolutionarily stable equilibrium under policy incentives and dynamic supply-demand feedback. By employing the replicator dynamic equation, it helps determine the evolutionary stability of different strategy combinations and identify the existence of ESS or MESS.

In fact, Ref. [34] proposed a typical algorithm process to describe the long-term evolutionary game, as demonstrated in Figure 4. Based on this, Ref. [34] adopted the evolutionary game algorithm in Figure 4 to investigate the equilibrium stability of a regional integrated energy market based on limited rationality and information access. Based on Figure 4, Ref. [30] investigated the dynamic adjustment process of the pricing strategies for two categories of generation enterprise groups, as demonstrated in Figure 5. In this figure, Cheng and Yu [30] found that, at this time, the evolution game system has a total of two long-term asymptotically stable equilibrium points (ASEPs), two long-term asymptotically unstable equilibrium points (AUEPs), and one saddle point (which is also an evolutionarily unstable equilibrium point as denoted by (x_s, y_s). Under the framework of Evolutionary Game Theory, the strategy evolution path of Power-Generation Enterprises is dynamically influenced by evolutionary strategies and payoff parameters. As shown in Figure 5a, the strategy combinations at the two ASEPs are MESS, namely: (0, 0) corresponds to both types of Power-Generation Enterprises adopting a base-price bidding strategy, while (1, 1) corresponds to both types of Power-Generation Enterprises adopting a high-price bidding strategy. Therefore, Figure 5a indicates that through analysis, it can be seen that the two types of Power-Generation Enterprise groups can achieve an evolutionarily stable state and possess a Nash equilibrium solution when they choose either the base-price bidding or high-price bidding strategy after a long-term evolutionary game. Figure 5b–d indicate that when the initial payoff distribution parameters of the system vary, the position of the green saddle point (x_s, y_s) also changes, but it always remains within the decision region [0, 1] × [0, 1]. The sizes of the two convergence domains formed by $①$ and $②$, and $③$ and $④$ (denoted as SL1 and SL2, respectively) also change accordingly. After a long-term evolution, one will tend toward a reasonable quote that people expect (i.e., the base-price quote), while the other will tend toward an irregular quote that people do not wish to see (i.e., the high-price quote). These will become the two evolutionary stable states of the system, and the probability of converging to these two states (equal to the area of the convergence domains) will change with the position of the saddle point. Through the above dynamic simulation and parameter analysis, it is evident that the strategy evolution paths of market participants exhibit patterns such as dual stable states, path dependency, and saddle point effects, driven by the principle of profit maximization, market feedback mechanisms, and policy regulation.

Based on Figure 5, Ref. [30] revealed that the final state to which the system evolves depends on whether the initial conditions of evolution (i.e., the value conditions of the payoff parameters u_i) are located in SL1 or SL2, meaning that the area where the initial state of the system is situated determines the system’s final evolutionary stable state. Therefore, we can adjust the values of some key parameters in the gain distribution matrix, so that we can realize the change of the location of the saddle point, which can ultimately affect the size and distribution of the entire convergence domain SL1 and SL2, so that the evolution trajectory of the system tends to a reasonable equilibrium node. For example, Ref. [35] revealed that the final evolutionary stable equilibrium state can be determined by changing certain key payoff parameters, which correspond to the government’s market supervision of electricity pricing. This means that the government determines the upper and lower limits of the electricity prices for Power-Generation Enterprises through economic analysis, ensuring that their profits remain within a reasonable range. On one hand, this guarantees that companies have appropriate profit and development space; on the other hand, it limits the profits of companies that report high prices, especially large Power-Generation Enterprises. Therefore, through government supervision, appropriately adjusting the payment parameters of the gains for both parties in the system can change the bidding payment profit matrix of the group game, making the electricity pricing decisions of various groups more rational and aligned with the actual development needs of the electricity bidding market. Overall, the advantages and features of the application when using Evolutionary Game Theory to study multi-group behavioral decision-making issues are illustrated in Figure 6.

Table 4

A summary of Evolutionary Game Theory applications in electricity and green certificate markets.

Paper	Players	Game Description	Advantages	Limitations
[36]	Multi-population in the electricity market	Develops a general model for long-term on-grid bidding strategies in the electricity market using evolutionary games	Provides a comprehensive framework for analyzing long-term bidding strategies in a dynamic market environment	May require further empirical validation to ensure applicability in real-world scenarios
[37]	Multiple players in continuous games	Proposes a co-evolutionary approach for detecting multiple Nash Equilibria in a single run within the context of electricity markets	Provides high-quality solutions and efficiency in terms of both solution quality and computational efficiency	Assumes continuous games and may not be applicable to discrete games
[33]	Various market participants in the electricity market	Reviews game-theoretic approaches applied to transactions in open and growing electricity markets	Offers an extensive overview of game-theoretic applications in electricity markets	The review may lack specific details on implementation challenges and practical considerations
[38]	Two players in a spatial Prisoner’s Dilemma Game	Introduces a preferential selection mechanism where players have a higher probability of learning from their contributing counterparts	Enhances cooperation by imitating contributing players	Focuses on a specific game and may not generalize to other scenarios
[39]	Platform, supporters, and initiator in reward-based crowdfunding	Constructs a three-party game model to analyze value co-creation and optimal pricing decisions under different crowdfunding modes	Offers insights into optimal pricing and mode selection for crowdfunding platforms	Focuses on crowdfunding and may not be generalizable to other contexts
[30]	Multi-group in electricity market scenarios	Analyzes the Nash equilibrium-based asymptotic stability in multi-group asymmetric evolutionary games within typical electricity market scenarios	Reveals dynamics behavior and multi-group evolutionary stable strategy in a three-dimensional strategy space	Specific to electricity market and may not apply to other markets
[40]	Generation-side enterprises in the electricity market	Investigates bidding behavior of generation-side enterprises using stochastic evolutionary games	Utilizes stochastic elements to better represent uncertainties in the bidding process	The complexity of the model may limit its scalability and computational efficiency
[41]	Governments, enterprises, and consumers in green supply chains	Builds a model considering green sensitivities and policy factors to analyze the evolutionary game	Identifies green sensitivity as a substitute for policy factors in green supply chain development	Limited to green supply chains and may not extend to non-green contexts
[42]	Self-interested agents in a multi-agent system	Study of the interplay between institutional incentives and networked structures in promoting prosocial behaviors using Evolutionary Game Theory	Demonstrates synergy between incentives and network structure, leading to improved efficiency in promoting prosocial behaviors	Focuses on regular graphs and may not capture complexities of other network topologies
[43]	Rational agents in a multi-agent system	Examination of Q-learning and FAQ-learning algorithms through the lens of evolutionary dynamics, using two-player two-action and three-action game models	Reveals underlying mechanisms of Q-learning and FAQ-learning, showing their convergence properties	Limited to the analysis of specific learning algorithms and may not generalize to other types of learning mechanisms

3.3. Stackelberg Game-Theoretical Method

The Stackelberg game, also known as the leader-follower game, is a dynamic form of game where players participate in a sequential order over time. In traditional game models, it is usually assumed that all players have the same and complete information, but they do not know the next moves of other participants [44].

The primary role of the Stackelberg game in electricity trading is to simulate and analyze the dynamic interactions among participants with varying market power [45], particularly in scenarios where leaders and followers are present. Leaders, such as electricity suppliers, retailers, or market operators, make decisions first, and followers, including consumers, Power-Generation Enterprises, or demand-response aggregators, respond based on the leaders’ decisions. These studies typically employ mathematical modeling and optimization algorithms to address strategic decision-making issues in the electricity market, such as demand response, energy scheduling, pricing strategies, and market operations. This game-theoretic model aids in understanding and predicting market behaviors and optimizing the functioning of the electricity market. Table 5 provides a summary of the application of Stackelberg game theory in the electricity and green certificate markets [46].

The payoff function for the Stackelberg game is described as $U_i(s_1, s_2, \cdots ,s_n)$. Based on this, when the expected payoff satisfies the following inequality, the Stackelberg game reaches an equilibrium state, which meets

(6)$u_i({s^{*}}_i, {s^{*}}_{-i}, h_t)\ge u_i(s_i, {s^{*}}_{-i}, h_t) \forall s_i\in S_i, i=1,2,\cdots ,n$

Based on Equation (6) and the summarizations in Table 5, we conduct a simulation study, as illustrated in Figure 7. This simulation study focuses on a Stackelberg game simulation within a green certificate (GC) electricity market, aiming to explore the dynamic strategic interactions between a leader (e.g., a regulatory authority) and multiple followers (e.g., Power-Generation Enterprises). The primary motivation is to examine how the leader’s policy or incentive decisions (captured by the strategy x) influence the followers’ green investment or green certificate bidding decisions (captured by the strategies y_i) over a period of 365 days. Key features of the model include:

• Sequential Decision-Making: The leader updates its strategy after observing the followers’ responses, exemplifying a leader-follower (Stackelberg) paradigm.

• Stochastic Elements: Random noise is added to reflect uncertainties in market conditions and operational environments.

• Convergence Behavior: Large-scale parameters (N = 500 followers, T = 365 days) highlight the scalability and stability of the simulation.

• Units: Time is expressed in days, while payoff and strategy are dimensionless but mapped to realistic policy or bidding contexts.

In this simulation, the leader’s payoff depends on the average green involvement among followers while incurring a quadratic cost for high policy intensities. Meanwhile, each follower’s payoff is determined by its chosen green strategy relative to the leader’s policy signal, incorporating a penalty for insufficient compliance. These settings allow a systematic demonstration of Stackelberg equilibrium formation and underscore the advantages of employing a leader-follower framework in the evolving green certificate market. Figure 7 demonstrates the simulation results for Stackelberg game-based decision-making in a green certificate electricity market, focusing on leader-follower interactions, payoff dynamics, and strategy convergence. In this figure, the detailed analysis of each subfigure is conducted as follows.

Figure 7a: This panel depicts the final-day payoffs of the leader (a single red star) and all 500 followers (blue dots). From the distribution, it is evident that while the leader’s payoff is relatively stable, the followers exhibit a tight cluster at higher payoff values. This indicates that, under the Stackelberg mechanism, the majority of followers converge to an optimal green strategy that maximizes their returns, whereas the leader achieves a moderate but steady gain—reflecting the trade-off between policy intensity and cost.

Figure 7b: The three-dimensional plot captures the day axis, the leader’s strategy x, and the average follower strategy $\overline{y}$. The steep shift in the first few days reveals rapid adaptation: the followers’ strategies escalate to near-maximum green engagement, while the leader’s strategy converges near zero or slightly negative. Such an outcome indicates that the leader can strategically reduce policy intensity once the followers have already aligned strongly with green investment, thus lowering its own penalty or cost.

Figure 7c: This heat map shows the matrix of follower strategies (y) across days and follower indices. The large uniform region in the figure indicates that almost all follower strategies consolidate around high (near 1.0) levels after just a short transient phase. The minimal color variation suggests that the entire follower population rapidly achieves a uniform equilibrium strategy, affirming the strong attractor properties of the Stackelberg equilibrium under high green preference.

Figure 7d: The multi-line evolution chart highlights how the leader’s strategy and a subset of follower strategies unfold over time. The leader’s x(t) line (in red) remains stable and significantly lower, whereas the average follower strategy (blue) and individual representatives (other colors) jump quickly to 1.0 or near 1.0, staying almost flat for the remainder of the simulation. This reflects the strongly incentivized environment, where early updates drive the followers’ green strategies to their upper bound.

Figure 7e: This panel compares the leader’s payoff with the mean follower payoff throughout the simulation. The followers’ payoff (blue) increases sharply at the initial stage, converging to a consistently higher value, whereas the leader’s payoff (red) stabilizes around 1.2. The drastic upward trajectory of follower payoff underscores the system’s capacity to facilitate robust gains for green-oriented participants, while the leader’s stable payoff suggests a balanced policy stance that neither overexerts financial burden nor remains under-incentivized.

Figure 7f: The three-dimensional scatter plot at the final day reveals the relationships among the follower strategy y, resulting payoff, and the index of each follower. Followers situated in the front (lower index) or the back (higher index) of the ordering exhibit nearly identical behavior: they cluster around very high strategy values (above 0.95) and yield high payoffs (around 1.45–1.55). The color mapping (from dark to light) signals that as the green strategy intensifies, the payoff also tends to rise and converge within a narrow range, reinforcing the notion that compliance with the leader’s signal is highly beneficial.

In summary, the simulation in Figure 7 convincingly demonstrates that employing a Stackelberg framework in a green certificate market facilitates swift convergence to near-unanimous high green strategy levels among followers, simultaneously maintaining a moderate yet stable payoff for the leader. This outcome underscores the distinct advantage of using a leader-follower paradigm to coordinate green investment and ensure compliance in complex, large-scale electricity markets. Future research can extend these findings by incorporating additional uncertain factors, multi-dimensional policy instruments, and real-world empirical data, thereby further validating the efficacy and adaptability of Stackelberg-based strategies in transitioning toward low-carbon energy systems.

Currently, the bidding used in the electricity market adopts the Stackelberg game. Before the bidding starts, the integrated energy system operator, as the leader in energy transactions, first takes into account the demand for green certificates, load demand, power dispatch requirements, etc., to set the energy price. Subsequently, users as followers in energy transactions, participate in the integrated demand response based on the electricity purchase price set by the integrated energy system operator, and feedback their final energy consumption demand to the operator [47]. The operator optimizes the system operation based on the feedback and finally sets the final transaction price [48].

Table 5

A Summary of Stackelberg game theory applications in electricity and green certificate markets.

Reference	Players	Game Description	Advantages	Limitations
[49]	Users and Utility Companies	Multi-timescale leader-following approach with Nash and Stackelberg games to optimize social profit in electricity markets	Proposes a novel approach to maximize market efficiency and social profit through strategic demand response management	Focuses primarily on theoretical modeling and may require further validation in practical scenarios
[50]	Energy Hub, Users, Electric Vehicles	Combines distributionally robust optimization with a Stackelberg game to manage renewable generation uncertainty in an energy hub	Offers a robust optimization framework to handle uncertainty and enhance the economic and environmental performance of an energy hub	The complexity of the model may increase computational requirements
[51]	Aggregator, Residential Customers	Utilizes a mixed-strategy Stackelberg game to manage demand response during peak load periods	Introduces a stochastic approach to demand response that accounts for customer uncertainty and behavior	The model’s applicability may be limited to specific types of customers and may require significant data for accurate predictions
[52]	Electricity Prosumers	Stackelberg and noncooperative games for pricing in joint carbon and electricity markets	Optimizes pricing for carbon and electricity, ensures compliance with emission restrictions	Assumes perfect competition, relies on user behavior prediction
[53]	Combined Heat-and-Power Unit Owners, Industrial Users	Stackelberg game for heat-electricity peak load shifting considering thermal delay	Accounts for thermal dynamics, facilitates multi-energy load shifting	Relies on accurate thermal delay estimation
[54]	Aggregator, Households	Stackelberg game to minimize wind curtailment and emissions through demand response	Reduces imbalances and emissions, utilizes residential heating flexibility	Depends on accurate wind and load forecasting
[55]	Generators and Microgrids	Stackelberg game model for optimal dispatching of electricity consumption considering demand response	Integrates economic and operational factors of smart grids	Assumes static renewable generation capacities
[56]	Distribution System Operator and Load Aggregators	Stackelberg game for optimizing demand response energy allocation	Maximizes control economy and minimizes power deviations	Concentrates on contracted demand response, not spontaneous
[57]	Renewable Investor and Local Investors	Stackelberg–Cournot game for strategic investment in energy infrastructure	Evaluates investment strategies and tariff incentives	Static investment analysis, lacks market dynamics
[58]	Combined Heat and Power Unit, Electricity Market Operator, Heat Market Operator	Stackelberg game model for bidding strategy of CHP units in district integrated heat and power grid	Calculates locational marginal prices, proves existence of Nash equilibrium in the game	Further research needed on the impact of heat and power grid interactions on bidding strategies

3.4. Markov Game-Theoretical Method

Markov games are typically used to describe the dynamic game processes of multiple intelligent agents with randomness [59]. In such games, it is generally assumed that agents are boundedly rational, and in each round of the game, each agent independently chooses their own strategy, receives an immediate reward based on the current state and the chosen action, and then the environment transitions to the next state according to a certain probability. Here, a typical algorithmic process of a Markov game is illustrated in Figure 8. Key elements of Markov games are explained as follows.

• Player set: $N=\left\{1,2,\cdots ,n\right\}$.

• State set: $S=\left\{s_1,s_2\cdots ,s_n\right\}$.

• Action set: $A_1,A_2,\cdots ,A_n, A=A_1\times A_2\times \cdots \times A_n$ where A_i is the action set for player i, and A represents the total action set in the Markov game.

• Transition function f: $S\times A\times S\to \left[0, 1\right]$, such that ${\displaystyle \sum f(s, a, s^{\prime }) =1}$ for all $s\in S, a\in A$.

• Reward function r: $S\times A\to ℝ, i=1,2,\cdots ,n$.

Based on the above key elements, in the process of studying the green certificate market using a Markov game model, market participants are modeled as game players, defining the player set. Each player formulates strategies based on their objectives: power producers may adjust green energy output to maximize profits, consumers may decide whether to purchase green energy, and policymakers may modify green certificate subsidies or quota policies to influence the market. By defining the state set, the model captures the overall market dynamics, including green certificate supply, demand, price levels, and policy implementation, providing a basis for players’ decision-making.

Players’ strategies impact market dynamics through a state transition function, which simulates the causal relationships between strategies and market states. Players select actions from an action set, driving state transitions over time. The model quantifies players’ payoffs through a reward function, such as the revenue of power producers from green certificate sales and subsidies, the environmental benefits consumers gain from purchasing green energy, and the societal benefits policymakers achieve through carbon emission reductions. Iterative optimization enables the model to derive the optimal strategies for each player under different policy scenarios and reveals the long-term evolution of market states.

In the field of Multi-Agent Reinforcement Learning, Markov games can be solved using different reinforcement learning algorithms, such as value-based Q-learning [43], Sarsa, DQN, policy-based Policy Gradient, and the Actor–Critic method that combines both. These methods can help agents learn how to choose the optimal strategy during the game process to maximize their cumulative rewards. Based on this, a Multi-Agent Reinforcement Learning system is demonstrated in Figure 9.

In multi-agent systems, the interactions among agents are typically constrained by the underlying topological structure. Ref. [59] proposed a graphical Markov game by modeling the topological structure as an undirected graph, to study how agents interact and make decisions considering long-term rewards and topological constraints within multi-agent systems. Utilizing a policy gradient-based algorithm, they aimed to identify the optimal strategy for each agent. As depicted in Figure 10, this Markov game algorithm is employed to investigate the decision-making processes of agents in multi-agent systems, taking into account both the long-term rewards and the constraints imposed by the topological structure.

3.5. Deep Reinforcement Learning Game-Theoretical Method

Deep reinforcement learning theory is an optimization algorithm for solving Markov games, used to optimize the training process of Markov Decision Processes (MDPs) [60]. The intelligent agent mainly includes four elements: performance measure Environment, Actuators and Sensors. In this deep reinforcement learning game system, a player’s strategy is represented as a policy matrix [61], where each element indicates the probability of the player choosing a certain action in a given state. Deep learning algorithms are then used to train this policy matrix. During training, the deep learning algorithm attempts to adjust the parameters within the policy matrix to maximize the rewards obtained by the player [62]. This process typically requires multiple iterations until the parameters in the policy matrix converge to a stable value [63]. After training, the policy matrix is used to generate the player’s strategy combinations in the game. This strategy combination can be represented as a list containing multiple actions, each of which is the optimal action calculated according to the policy matrix based on the current state [64].

In game theory, Multi-Agent Reinforcement Learning (MARL) algorithms focus on enabling individual agents to achieve their goals in multi-agent environments by addressing collaborative and competitive relationships among agents [65]. In the context of the green certificate market, MARL algorithms can be applied to tackle issues such as balancing supply and demand, optimizing subsidy policies, and designing strategies for energy producers, consumers, and policymakers. Given the market’s dynamic characteristics, including price fluctuations and policy variability, tailored MARL algorithms provide effective solutions for these challenges [66]. Table 6 primarily lists some typical algorithms and analyzes their advantages and disadvantages, reflecting the diversity and complexity of the field of Multi-Agent Reinforcement Learning, with each algorithm having its specific application scenarios and limitations.

To address Markov Decision Processes (MDPs), a commonly used mathematical method is the Bellman Equation. This method describes the relationship between cumulative rewards obtained by market participants in different market states [67]. Specifically, the Bellman Equation can calculate the value function of a market state, representing the maximum cumulative reward participants can achieve by adopting the optimal strategy in the current state. By solving the Bellman Equation, market participants can optimize their strategies to achieve supply-demand balance, profit maximization, and efficient attainment of policy objectives in the green certificate market [68]. For example, the Bellman Expectation Equation is shown as

(7)$V^{\pi }(s)={\displaystyle \sum _{a\in A}\pi (a|s)}\left[R(s,a)+\gamma {\displaystyle \sum _{s^{\prime }\in S}P(s^{\prime }|s,a)V^{\pi }(s^{\prime })}\right]$

This equation is used to calculate the state-value function V(s) under a given policy $\pi$ following the policy and the weighted sum of the value of the next state $s^{\prime }$. It enables power producers to analyze the benefits of adjusting green energy output under current policies and supports consumers in assessing the long-term environmental benefits of purchasing green certificates.

The Bellman Optimality Equation is described as

(8)$V^{*}(s)=\underset{a\in A}{\max }\left[R(s,a)+\gamma {\displaystyle \sum _{s^{\prime }\in S}P(s^{\prime }|s,a)V^{\pi }(s^{\prime })}\right]$

This equation in (8) describes the state-value function V*(s) under the optimal policy. It indicates that the optimal value of state s is the weighted sum of the immediate reward obtained by taking the optimal action a and the optimal state value of the next state $s^{\prime }$ after entering it. This equation helps policymakers optimize subsidy policies or quota systems to ensure long-term market stability while maximizing carbon reduction and social benefits. Overall, the comparison of game-theoretical methods explained above can be summarized as shown in Table 7.

Table 6

Typical advantages and disadvantages of MARL algorithms.

Algorithm Name	Description	Advantages	Disadvantages
IQL [3]	Agents learn independently using single-agent Q-learning, ignoring others.	Simple and straightforward approach.	Ineffective in scenarios requiring coordination.
JAL [69]	Agents learn a joint action-value function considering all agents’ actions.	Good coordination.	High computational complexity and scalability issues.
VDN [70]	Decomposes the joint value function into a sum of individual agent value functions.	Reduces complexity of multi-agent learning.	May perform poorly in tasks lacking independence among agents.
COMA [71]	A “centralized training, decentralized execution” algorithm for discrete actions.	Fewer signal and strategy coordination issues.	High computational cost and not suitable for continuous action spaces.
QMIX [72]	Overcomes IQL limitations with a mixed value network and a novel value decomposition architecture.	Coordinates actions while maintaining low-dimensional complexity.	Limited function fitting capability for non-monotonic tasks.
MAPPO [73]	A multi-agent reinforcement learning algorithm for continuous action spaces.	High operational efficiency and data sample efficiency.	May perform poorly in highly nonlinear environments.
MADDPG [74]	A “centralized training, decentralized execution” algorithm for continuous action spaces.	Suitable for complex environments and learns deterministic policies.	High training cost and difficulty in handling large-scale problems.
MARL [75]	Multi-agent reinforcement learning involving multiple agents interacting in a single environment.	Handles complex interactions and coordination among agents.	High computational complexity and scalability challenges.
UNMAS [76]	Designed for cooperative scenarios where the number and size of action sets vary.	Adapts to dynamic changes in agent numbers and action sets.	May underperform in static environments.
MADDPG-C [77]	An extension of MADDPG for edge caching in distributed cloud environments.	Improves edge cache hit rate and reduces terminal device latency.	Sensitive to environmental changes and requires extensive training data.
IPPO [78]	Independent Proximal Policy Optimization for multi-agent systems.	Agents train independently without centralized training.	May be ineffective in scenarios requiring high levels of coordination.

4. The Impact on Power-Generation Enterprises Under Green Certificate Trading

The introduction of the GC market has not only promoted the widespread application of renewable energy but also altered the cost structure and market behavior of PGEs by influencing the competitive structure and pricing mechanisms of the Electricity Market (EM).

The interaction between the GC market and the EM is manifested at multiple levels: the GC market provides additional economic incentives for renewable energy generation, while the price fluctuations and supply-demand balance of the EM directly affect the stability of the GC market. Furthermore, the bidding strategies of PGEs are influenced by some factors including market demand, policy support, capital costs, risk management, and environmental benefits [79].

4.1. Game Research on Power-Generation Enterprises in Green Certificate Trading

Currently, Power-Generation Enterprises focus their research on green certificate trading primarily on how to promote the consumption of renewable energy through such trading. In terms of integrating green certificate trading with carbon trading, Ref. [80] conducted an in-depth analysis of the interaction mechanisms between green certificates and carbon trading, proposing an optimized bidding strategy model for the economic benefits of Virtual Power Plants to ensure optimal economic outcomes in the competitive green certificate and carbon markets. Ref. [81] developed models considering both green certificate trading and carbon trading processes under the “dual-carbon” target, describing their interaction mechanisms through system dynamics models. The synergy between electricity and carbon can increase the installed capacity of renewable energy and boost the overall revenue of the system. Ref. [82] established and expanded the existing dynamic computable general equilibrium model by incorporating carbon trading systems and green certificate trading systems into the modeling framework. The findings from this research contribute to the understanding of how policy instruments can be designed and implemented to optimize the balance between economic growth and environmental sustainability. Ref. [83] developed a regional integrated energy system model that facilitates the trading of electricity, gas, heat, and cooling. This model is designed to optimize the allocation and exchange of various energy resources within a defined region, enhancing the efficiency and sustainability of the energy supply chain. By leveraging the equivalence between carbon emissions reductions and green certificate transactions, the strategy encourages a market-driven approach to energy consumption and production that takes into account the carbon footprint, ultimately contributing to the broader objectives of carbon neutrality and environmental sustainability.

In terms of optimizing the green certificate trading mechanism, Ref. [84] integrated delay differential equations into the green certificate market, conducting a comprehensive analysis of the structural relationships and feedback mechanisms within and between markets. This approach has elucidated the complex dynamics between carbon prices, green certificate prices, and electricity prices under various coupling mechanisms, providing valuable insights for policymakers and market participants. Ref. [85] proposed a market equilibrium model that takes into account both the energy market and the tradable green certificate market, employing a two-stage analysis comprising day-ahead and real-time markets. A bi-level model structure has been established, which comprehensively considers market clearing rules, power system operations, and the uncertainty of renewable energy sources. This framework provides a thorough and practical tool for analyzing the strategic behaviors of renewable energy. Ref. [86] proposed a blockchain-based decentralized platform for the issuance and trading of RECs. By tokenizing RECs, the study demonstrates the potential of blockchain technology in enhancing the reliability and security of REC issuance and tracking systems, while also reducing operational costs and improving the transparency and traceability of transactions. Ref. [87] designed a blockchain-based direct power-purchase (DPP) transaction method that integrates the peak shaving characteristics of industrial users and the green certificate system, completing the relevant transactions on the blockchain platform. They proposed a DPP market structure and a DPP transaction mechanism based on green certificates and peak shaving characteristics. By leveraging blockchain technology, the transparency and reliability of DPP are enhanced. Furthermore, considering green certificates and peak shaving characteristics, the method provides additional value for both industrial users and renewable energy companies.

Regarding green certificate trading and policy formulation, Ref. [88] employed a difference-in-differences model, complemented by robustness checks, to evaluate the financial and green patent licensing data of resource-based listed companies in China. They concluded that policies increasing the revenue of resource-intensive industrial enterprises, alleviating financial constraints, providing subsidies, and enhancing corporate research and development incentives foster green innovation. Ref. [89] proposed an Actor-Critic Off-Policy Correction reinforcement learning framework that improves policy evaluation and convergence in deep reinforcement learning by correcting discrepancies between policy and collected data. It achieves higher returns and stability in various simulations. Based on this, the green certificate issuance and trading process is shown in Figure 11.

4.2. The Impact of Cost Structure on Power-Generation Enterprises

The impact of green certificate markets on the cost structure of PGEs is primarily reflected in areas such as energy structure adjustment, internalization of environmental costs, increased carbon emission costs, and market competition. Firms’ behavioral responses exhibit significant differences under varying policies and market conditions.

In terms of energy structure adjustment costs, under a high-subsidy scenario, PGEs accelerate their transition to clean energy, which may lead to a short-term increase in costs. However, in the long run, costs are likely to decline due to technological advancements and economies of scale [90]. Using a threshold effect model, Ref. [91] analyzed the impact of government subsidies on renewable energy investment and found that high subsidies significantly enhance firms’ incentives to invest in clean energy, especially in energy-intensive regions where the effect of subsidies is more pronounced. Conversely, under a low-subsidy scenario, firms show insufficient investment motivation, leading to slower energy structure adjustments and persistently high costs. Ref. [92] simulated the removal of cross-subsidies and analyzed its effects on economic performance, CO₂ reduction, industrial structure, and social welfare, concluding that an appropriate carbon tax would promote low-carbon development in China. Additionally, the speed of technological progress also affects cost outcomes. Accelerated technological progress significantly reduces the cost of green energy technologies, making structural adjustments more economically viable. However, if technological progress lags, enterprises face sustained high costs, which dampens their motivation for transformation. Ref. [93] emphasized the critical role of technological progress in driving global energy transitions, highlighting the importance of rapid innovation in wind and solar technologies in reducing costs.

Regarding internalization of environmental costs, the level of carbon tax directly influences corporate behavior. Under a high-carbon-tax scenario, enterprises face significant cost pressures, forcing them to accelerate structural adjustments and reduce reliance on high-emission energy. Conversely, under a low-carbon-tax scenario, the cost pressure on enterprises is limited, leading to low motivation for transition and continued reliance on high-emission production structures. Ref. [94] utilized a differential game model to conclude that high carbon taxes encourage firms to innovate and share low-carbon technologies, resulting in greater emissionsreduction benefits, whereas low carbon taxes provide insufficient incentives for corporate transformation. Similarly, Ref. [95] employed a dynamic equilibrium model to examine the effects of carbon taxes on emissions reduction and economic performance in high-emission industries, finding that high tax rates promote structural optimization within industries.

Moreover, carbon emission costs are closely related to the maturity of carbon trading markets. Under the guidance of low-carbon policies, the electricity sector must explore and refine market mechanisms, including restricting the production of energy-intensive and high-emission enterprises [96]. With the operation of carbon trading markets, carbon pricing will be linked to power-generation costs [97]. With the operation of carbon trading markets, carbon pricing will be linked to power-generation costs [98]. Using a difference-in-differences model, Ref. [99] analyzed the impact of carbon allowance allocation and pricing on corporate behavior, demonstrating that carbon trading policies, through reduced free allowances and higher carbon prices, incentivize firms to improve their financial performance through low-carbon technology investments.

The operation of green certificate markets also alleviates financial pressures on enterprises, but the effectiveness of this depends on market activity. In highly active markets, stable green certificate prices improve corporate cash flow, further accelerating green investments. Conversely, in volatile markets, unstable green certificate prices increase revenue uncertainty, intensifying financial pressures and constraining investment decisions. Ref. [100] analyzed the impact of market volatility on green investments using a GARCH-based quantile regression model on daily data. The study revealed that during periods of market instability, the attractiveness of green certificate markets to investors significantly declines, with funds shifting to more stable conventional energy markets.

As market competition intensifies, Power-Generation Enterprises face mounting profitability pressures. In mature markets, firms enhance their competitiveness through technological innovation and cost optimization. However, in less mature markets, firms often resort to lowering green certificate prices to gain market share, resulting in shrinking profit margins and weakened long-term competitiveness. Ref. [101] studied the green certificate trading mechanism and found that the environmental damage caused by coal-fired PGEs can be internalized into corporate costs through this mechanism. Consequently, PGEs must take greater responsibility for environmental pollution and greenhouse gas emissions, thereby increasing their operating costs [102].

In conclusion, policy intensity, market maturity, and the speed of technological progress are the core factors influencing the cost structure and behavioral choices of Power-Generation Enterprises. Under scenarios of high subsidies, stringent carbon taxes, and active markets, firms tend to engage in green investments and technological innovation, driving cost reductions and enhancing competitiveness. Conversely, under low subsidies, relaxed carbon taxes, and less mature markets, firms exhibit low motivation for transformation, leading to persistently high costs and slow progress in green transitions. Thus, policy designs should dynamically adjust based on market and technological conditions to balance short-term cost pressures with long-term low-carbon transition objectives.

4.3. The Impact of Bidding Strategies on Power-Generation Enterprises

The impact of the Green Certificate Market on the bidding strategies of PGEs is mainly reflected in the following aspects:

• (1). Market Demand and Policy Support. If there is high market demand for green certificates or if policies encourage the use of renewable energy, PGEs may raise the price of green certificates in bidding.

• (2). Capital Costs and Financing Channels. If PGEs can obtain lower financing costs or have stable funding sources, they may adopt more aggressive strategies in bidding.

• (3). Risk Management Strategies. Enterprises may hedge by purchasing carbon emission rights or other related financial products to lock in their power-generation costs, thereby gaining greater flexibility in bidding.

• (4). Environmental Benefits of Power-Generation Enterprises. Green certificates represent the environmental benefits of renewable energy generation, and PGEs can obtain additional revenue by selling green certificates. This environmental benefit may allow PGEs to secure higher prices in bidding, thereby improving their economic benefits.

• (5). Carbon Emission Costs of Power-Generation Enterprises. After the operation of the carbon trading market, the carbon price will be coupled with power-generation costs, promoting the transformation of China’s energy structure [103]. If PGEs can reduce their carbon emission costs by selling green certificates, they may adopt more aggressive strategies in bidding to compete for a larger market share [104].

5. Game Measures to Enhance Competitiveness of Power-Generation Enterprises

Currently, the academic community has conducted extensive research on the strategic optimization of Power-Generation Enterprises in response to market and policy changes, particularly on how to optimize operations [105], control costs, enhance market competitiveness, and achieve sustainable development under the broad context of carbon emission reduction and green transformation [106]. As depicted in Figure 12, the relationship between Power-Generation Enterprises and the electricity market as well as green certificate trading is interdependent and complementary. By optimizing these relationships, Power-Generation Enterprises can better adapt to market changes, enhancing their competitiveness and sustainability in the new environment.

Incorporating the carbon market, Ref. [2] established a distributed market model that integrates electricity and carbon emission rights trading, proposing a scalable fully distributed algorithm to solve the model. The algorithm eliminates the need for any central coordination layer, ensuring global power balance and emission constraints, effectively reducing transaction costs and ensuring transaction transparency. Ref. [107] proposed a tri-level planning approach that takes into account carbon emission flow, designed to coordinate the planning of integrated electricity-hydrogen-gas systems. The approach quantifies the distribution of carbon emissions at each energy hub within the coupled network, effectively reducing the carbon emissions of the integrated system. Ref. [108] proposed a coordinated low-carbon dispatching method on the source-demand side based on an Integrated Demand Response Exchange mechanism, establishing a two-stage low-carbon dispatching model. This approach incentivizes user participation in low-carbon demand response, facilitating interaction between users and Power-Generation Enterprises, optimizing the allocation of benefits, and enhancing social welfare. Ref. [109] established a dual-layered model, with the upper layer being a multi-market profit maximization model for Power-Generation Enterprises, and the lower layer encompassing the settlement models for the day-ahead electricity market and the bi-directional carbon market. This model accelerates the solution process through a partial linearization method, while also considering the multi-market strategic behaviors of PGEs in both the electricity and carbon markets.

Although existing research has provided insights into the strategy formulation of Power-Generation Enterprises in the face of market and policy changes, against the backdrop of increasingly strengthened green energy and carbon-reduction policies [110], Power-Generation Enterprises need new strategies to adapt to this transformation. In particular, regarding how Power-Generation Enterprises can formulate optimal electricity market trading strategies under the joint action of various new policies, this paper will focus on analyzing the specific methods for Power-Generation Enterprises to enhance market competitiveness.

5.1. Optimization of Cost Structure

Cost control is a key factor in corporate operations, as it is directly related to a company’s profit levels and plays a crucial role in shaping its market competitiveness. The cost structure of Power-Generation Enterprises generally includes fuel costs, operation and maintenance costs, environmental compliance costs, financial costs [108], and human resource costs, among others. In the face of rapid changes in the energy industry, Power-Generation Enterprises must adopt innovative cost-management measures to adapt to market changes and maintain competitiveness.

Firstly, Power-Generation Enterprises should cultivate a cost consciousness among all employees, integrating the concept of cost control into the corporate culture. Companies should strengthen their staff’s understanding of modern cost management through training and education, ensuring that every employee recognizes their role in cost control and actively participates. By enhancing the skills and awareness of employees, waste can be reduced from the source and efficiency can be improved. Secondly, companies need to optimize operational management and establish an efficient cost control system. This includes streamlining cost control positions, reasonably allocating responsibilities, and granting cost control personnel the appropriate authority to effectively implement cost-saving measures. Additionally, companies should regularly review and update cost control systems to ensure they keep pace with market changes and policy updates. Furthermore, Power-Generation Enterprises should construct a comprehensive cost control organization responsible for overseeing and guiding cost control activities across the company, clarifying the specifics of control [111]. This organization should focus on improving corporate benefits, delve into various operational aspects of the company, ensure that cost expenditures are effectively controlled, and reduce unnecessary waste [112]. Lastly, Power-Generation Enterprises should adopt advanced cost control methods, often in combination with game-theoretic modeling approaches [113], considering electricity purchase costs, green certificate trading costs, and electricity sales revenue, to derive optimal strategies for low-cost absorption [114]. A comprehensive analysis and control of corporate cost optimization should be conducted. Beyond price competition, Power-Generation Enterprises also need to focus on and optimize the non-price attributes of their services, such as service quality [115,116], reliability, environmental standards, and customer service, to meet the needs of different consumer groups [117].

5.2. Flexible Adjustment of Bidding Strategies

In the context of fierce competition and frequent policy changes in the green certificate and electricity markets, Power-Generation Enterprises must flexibly adjust their bidding strategies to adapt to market changes and enhance competitiveness [118]. Game theory, as an effective analytical tool, can assist Power-Generation Enterprises in constructing game models based on their specific situations, thereby adjusting bidding strategies [119].

Taking the research work in [120] as an example, we observe how Power-Generation Enterprises adjust their bidding strategies through Evolutionary Game Theory under two market settlement mechanisms: the Market Clearing Price (MCP) and Pay as Bid (PAB). Under the MCP mechanism, studies find that Power-Generation Enterprises tend to adopt high-price strategies; whereas under the PAB mechanism, adjusting the compensation coefficient α can guide Power-Generation Enterprises to adopt more rational bidding strategies, thereby reducing the electricity costs for users. This finding not only validates the practical application of theoretical models in the green certificate and electricity markets but also provides empirical references for Power-Generation Enterprises to flexibly adjust their bidding strategies. Through such strategic adjustments, companies can better adapt to market changes, optimize their economic benefits, and maintain a competitive edge in the market competition.

Furthermore, Power-Generation Enterprises can participate in the spot market by declaring different methods such as quantity and price, or quantity without price, to study and adjust the company’s optimal bidding strategy to ensure that while meeting market demand [121], the maximization of economic benefits is achieved. In addition to price competition, Power-Generation Enterprises also need to pay attention to and optimize the non-price attributes of their services, such as service quality, reliability, environmental standards, customer service, etc., to meet the needs of different consumer groups [122]. Through these strategic adjustments, companies can better adapt to market changes, optimize their economic benefits, and maintain a competitive edge in the market competition.

5.3. Adapting to Dynamic Reward and Punishment Mechanisms

To cope with dynamic reward and punishment mechanisms, Power-Generation Enterprises must adopt a series of strategic actions to ensure their long-term competitiveness and profitability. Firstly, companies need to closely monitor changes in government policies, particularly incentives and penalties related to carbon reduction. This requires the establishment of dedicated teams to track and analyze policy changes and their potential impacts. In response to specific policy adjustments, enterprises should rely on professionals to develop corresponding evolutionary game models to identify optimal strategies under new regulations. For instance, Ref. [98] proposed an optimal real-time pricing model for electricity supply based on a dynamic reward-punishment mechanism. This model incorporates dynamic rewards and penalties to optimize real-time pricing strategies, guiding users to adjust their electricity consumption behaviors to achieve supply-demand balance and maximize user utility.

To achieve a win-win situation for environmental and economic benefits, Power-Generation Enterprises should proactively adjust their business strategies and maintain flexibility to align with government incentives and penalties [123]. In addition, the government can encourage and regulate corporate ecological innovation behavior through the implementation of subsidy and punishment mechanisms. Power-Generation Enterprises should make full use of this mechanism as a driving force for the development and application of environmental protection technologies. In this way, companies can enhance their sustainable development capabilities while following government policy directions [124].

In the EU, enterprises primarily rely on carbon trading markets and market-based electricity pricing mechanisms for flexible optimization. The carbon trading system (EU ETS) and mandatory quota schemes serve as core policies to guide enterprises toward self-driven carbon reduction through market-based methods. Companies participate in carbon allowance trading and leverage technological innovations to lower carbon emissions. This approach significantly stimulates innovation and enhances long-term competitiveness but imposes considerable economic pressure on high-carbon enterprises, particularly in the short term, due to high transition costs. Conversely, China’s strategy is more policy-driven, relying heavily on government intervention and direct incentives. Policies such as subsidies, carbon tax pilots, and mandatory quotas play a strong regulatory and guiding role, enabling rapid compliance and promoting green technology adoption. However, this heavy reliance on policy may, to some extent, limit enterprises’ capacity for independent innovation and their adaptability to market changes. By comparing the differences between the EU and China in electricity supplier behavior, regulatory mechanisms, and market operation, the advantages and limitations of each model are clarified, offering insights into the complementary relationship between market mechanisms and policy tools.

Differences in market mechanisms and electricity pricing further amplify the divergence in corporate decision-making behaviors. The EU exhibits a higher degree of market liberalization, granting enterprises greater decision-making autonomy. Market-driven pricing mechanisms reflect supply and demand dynamics through real-time electricity pricing and dynamic bidding, compelling enterprises to continuously optimize bidding strategies to remain competitive. In contrast, China’s electricity market remains in a transitional phase of marketization, with electricity prices significantly influenced by government regulation. Corporate strategy adjustments in China primarily rely on reward and punishment mechanisms, making decision-making more policy oriented. These differences profoundly impact the flexibility and adaptability of enterprises in the two markets [125].

In terms of innovation and adaptability, EU enterprises prioritize long-term technological innovation and competitive advantage. Driven by carbon market pressures, they invest heavily in green technologies, such as renewable energy generation, storage solutions, and carbon capture, utilization, and storage (CCUS), to reduce emissions and enhance competitiveness. By contrast, Chinese enterprises, driven by government subsidies, accelerate the development and application of green technologies but primarily focus on meeting compliance targets and obtaining policy incentives in the short term. While this approach promotes rapid green technology adoption, it still leaves room for improvement in fostering independent innovation and market competitiveness.

Furthermore, in responding to dynamic reward and punishment mechanisms, EU and Chinese enterprises exhibit distinct strategies [126]. EU companies rely on market-based mechanisms to flexibly adjust production strategies and prices, actively avoiding the economic costs of high emissions and demonstrating high adaptability. In contrast, Chinese enterprises depend heavily on government-established subsidies and carbon taxes to maximize compliance-driven profits, with strategic adjustments strongly influenced by policy direction. These differences reflect the profound impact of contrasting policy models on corporate behavior.

Both models have distinct advantages and limitations, and their differences highlight valuable lessons for global energy markets. The EU’s market mechanisms emphasize long-term innovation and competitiveness, making them a reference point for regions with established markets aiming to incentivize sustainable development. Conversely, China’s policy-driven model showcases the strength of rapid government intervention, providing a viable pathway for emerging economies to achieve swift renewable energy adoption and emission reductions. These complementary approaches suggest that global energy policy design could benefit from integrating both strategies. For instance, countries in the early stages of energy transition might prioritize policy-driven tools to establish foundational infrastructure, before gradually incorporating market-based mechanisms to sustain innovation and competitiveness.

This comparative insight underscores the need for international cooperation and alignment, particularly as global energy markets become increasingly interconnected through cross-border carbon trading and green certificate systems. Aligning policies and trading frameworks across regions could enhance market efficiency, reduce compliance barriers for multinational enterprises, and promote a more cohesive transition toward a low-carbon global economy. By leveraging both market mechanisms and policy tools, countries can create adaptable strategies tailored to their unique economic and environmental contexts, fostering global collaboration in energy sustainability.

Overall, EU and Chinese power suppliers exhibit significant differences in behavioral patterns and policy responses. The EU’s market-driven approach fosters long-term innovation and competitiveness by incentivizing self-driven strategies and technological advancements. However, this comes with higher economic pressures on high-carbon enterprises, particularly during the transition phase. In contrast, China’s policy-driven model demonstrates strong enforcement capabilities and achieves rapid compliance and emission-reduction targets through direct government intervention. While this approach accelerates green technology adoption, it underscores the need for greater market liberalization and the enhancement of enterprises’ capacity for independent innovation. These differences highlight the complementary strengths of both models, suggesting that a balanced integration of market mechanisms and policy tools could serve as a valuable framework for addressing global energy transition challenges.

5.4. Strengthening Forward-Looking Planning

In the evolving energy policy environment, Power-Generation Enterprises are facing unprecedented challenges [127]. To maintain competitiveness and promote sustainable development, these companies must enhance their forward-looking planning. This requires businesses not only to respond to current policies but also to anticipate potential policy changes and formulate contingency plans accordingly [128]. For instance, when the “Notice on Doing a Good Job in the Full Coverage of Renewable Energy Green Power Certificates to Promote the Consumption of Renewable Energy Electricity” stipulates a 2-year usage period for green certificates, market participants have rushed to sell their certificates, causing a significant drop in the price of green certificates and a notable impact on the costs of Power-Generation Enterprises. Under such circumstances, companies that can plan ahead and adapt quickly to market changes are better positioned to mitigate risks and minimize losses.

Therefore, Power-Generation Enterprises should continuously enhance their predictive and planning capabilities. By self-studying and researching the development trends of domestic and international electricity market, green certificate markets, and carbon markets, companies can formulate forward-looking strategic plans based on their own circumstances [129]. This includes predictive analysis of future market mechanisms, policy orientations, and technological changes, and building response measures accordingly. Through such strategies, companies can be more composed when facing new policies, ensuring that their business activities comply with policy regulations while optimizing their market positioning and competitiveness using new market mechanisms [130].

Through these channels, Power-Generation Enterprises can more accurately understand the government’s policy intentions and promptly obtain information on policy changes, thereby better adapting to policy shifts. This also helps companies to provide constructive suggestions during the policy-making process, influencing the final direction of policies to better adapt to the future market environment [131].

5.5. Summary of Policy Mechanisms and Stakeholder Behavior Analysis in the Green Transition

In the process of green transition, the design and implementation of policy mechanisms play a pivotal role in guiding behavioral adjustments among key stakeholders in the energy market. By integrating diverse policy instruments with market mechanisms, these interventions leverage incentives, constraints, and regulatory measures to drive the coordinated transition of Power-Generation Enterprises, governments, and electricity users on both the supply and demand sides. Leveraging the system dynamics approach enables a dynamic perspective to analyze the complex interactions among stakeholders, revealing how policy interventions influence changes in returns, strategy evolution pathways, and long-term stability through feedback loops. This provides a robust scientific foundation for policy optimization and the development of an efficient green energy system.

As key stakeholders in the energy market, Power-generation Enterprises are significantly influenced by the dual forces of market mechanisms and policy interventions. Based on literature [132], and utilizing policy scenarios and the system dynamics approach, the strategic decisions and revenue changes of power suppliers under different RPS implementation levels are summarized in Table 8. Supported by green electricity subsidies and rising carbon costs, Power-Generation Enterprises achieve revenue growth through increased green investments or optimized production structures. However, these behaviors are largely dependent on the continuity of policies and the stability of market conditions.

To better adapt to evolving policies and market dynamics, Power-Generation Enterprises must respond flexibly to changing market conditions and policy requirements. The opening of the green certificate market not only provides an additional revenue stream but also strongly incentivizes companies to transition toward greener operations. Particularly, as the enforcement of RPS policies intensifies, green certificate trading plays a pivotal role in supporting the low-carbon development pathways of power suppliers. Meanwhile, intensified competition in the energy market drives companies to focus more on technological innovation and operational efficiency to maintain their competitive edge in an increasingly challenging environment [12].

In the energy market, governments act as rule-makers and policy implementers, and their decisions play a critical role in market operation and development. Table 9, based on references [133,134], summarizes the impacts of different policy interventions on government finances, market evolution pathways, and stability. Effective policy design requires a balanced consideration of short- and long-term economic costs, environmental benefits, and market stability.

Carbon pricing mechanisms reduce high-emission activities through cost pressure while significantly increasing government fiscal revenue, facilitating a transition from “high emissions and high taxes” to “low emissions and low taxes”. As a cost-effective mitigation tool, carbon pricing is particularly suitable for markets where natural gas can rapidly replace coal. However, excessively high carbon prices may increase the financial burden on enterprises, compromise market stability, or even lead to firm withdrawal [135]. Thus, carbon pricing should be aligned with rational pricing strategies and international cooperation mechanisms to more effectively guide the market toward low-carbon transformation.

Renewable energy subsidies and mandatory green certificate quotas focus on directly enhancing renewable energy market penetration by increasing policy incentives, thereby accelerating energy structure transformation. These measures enable the market to evolve from “low renewable energy shares” to “high renewable energy shares”. In low-carbon price scenarios, such policies effectively replace high-emission energy sources and support decarbonization objectives. However, they require substantial fiscal expenditures, and their marginal abatement costs are generally higher than those of carbon pricing. Under high-carbon price conditions, the marginal abatement benefits of renewable energy may gradually diminish, necessitating a balance between fiscal sustainability and policy effectiveness through optimized subsidy levels and coverage.

Time-of-use pricing and market-based pricing mechanisms exhibit significant advantages in improving market efficiency. By accurately reflecting supply-demand dynamics and energy costs, these mechanisms effectively alleviate government fiscal burdens and promote the transition from “fixed pricing” to “market-based pricing”. However, these mechanisms place higher demands on the adaptability of enterprises and consumers. Policymakers must develop supportive measures to help vulnerable groups manage the potential impacts of price fluctuations.

Overall, carbon pricing mechanisms are suited for achieving rapid large-scale emission reductions, renewable energy subsidies drive long-term structural transformation, and time-of-use and market-based pricing mechanisms excel in enhancing efficiency and reducing fiscal burdens. Different policy tools should be coordinated based on specific needs to achieve sustainable development goals while ensuring economic viability and social equity.

Electricity users’ consumption behavior and demand patterns are directly influenced by market mechanisms and policy interventions, making them a critical component in demand-side adjustments within the energy market [136]. Table 10 highlights user behavior changes under scenarios such as time-of-use pricing, green certificate cost pass-through, carbon tax transmission, and dynamic price adjustments. Time-of-use and dynamic pricing mechanisms effectively guide users to optimize their electricity-consumption patterns, progressively increasing the share of green electricity. Carbon taxes, transmitted indirectly through electricity prices, reduce high-energy-demand consumption, while the reasonable pass-through of green certificate costs further enhances users’ environmental awareness. Overall, price mechanisms have a significant impact on shaping user behavior and serve as a core tool for driving demand-side transformation [137].

The analysis of the three tables reveals that market mechanisms and policy interventions have a profound impact on the behavior of Power-Generation Enterprises, governments, and electricity users. The green transition of Power-Generation Enterprises is driven by a combination of market incentives and policy pressures, with dynamic adjustment policies playing a crucial role in enhancing long-term competitiveness. Governments, in designing and implementing policies, must balance short-term benefits with long-term objectives. Dynamic policy tools are more effective in aligning market efficiency with policy goals but require adequate fiscal resources and the adaptability of market participants for successful implementation. Electricity users, as key demand-side actors, are most sensitive to price mechanisms [138]. Dynamic pricing adjustments and time-of-use pricing effectively guide users to optimize their electricity consumption, driving the demand side toward green consumption patterns. Overall, the synergy between market mechanisms and policy interventions is the core driver of energy market decarbonization, with dynamic regulatory policies being better suited for achieving long-term green transition objectives.

6. Market Challenges and Policy Guidance

6.1. Challenges and Development Potential in China’s Green Electricity Market

China’s green electricity market is still in its infancy, facing numerous challenges yet showing immense development potential. As global attention to renewable energy and carbon emission reductions deepen, the demand for green certificates is expected to increase steadily, bringing new opportunities for market expansion [139]. Ref. [140] indicates that policy-driven renewable energy certificate markets play a critical role in promoting energy transitions and achieving carbon-reduction targets. However, realizing the full potential of this market requires addressing several key issues, including insufficient market scale and liquidity, underdeveloped trading platforms, and a lack of international competitiveness. These challenges not only hinder the market’s standardization but also limit the broader adoption and application of green electricity.

The following analysis will examine the underlying causes of these challenges through existing literature and game-theoretical models while exploring potential policy and technical interventions. This approach aims to provide valuable theoretical support and practical insights for understanding market bottlenecks and promoting the sustainable development of the green electricity market.

• (1). Insufficient market scale and liquidity.

The small scale of the Green Electricity Certificate (GEC) market limits liquidity and undermines the effectiveness of price discovery mechanisms. This issue is common in early stages of energy markets worldwide, especially when policy frameworks are nascent and market participants are few. Ref. [141] using a three-stage Stackelberg game model analyzed the role of government subsidies in optimizing market behaviors and improving liquidity in renewable energy trading markets. The study demonstrated that appropriate government interventions, such as reducing transaction costs and setting price floors, could stimulate market activities and enhance confidence among participants. Similar policy mechanisms and game-theoretical insights could address the low liquidity of China’s GEC market, paving the way for international integration and improving transaction efficiency and price stability.

• (2). Lack of clear trading rules and regulatory frameworks.

China’s green certificate market currently lacks clear trading rules and regulatory frameworks, resulting in uncertainty among participants and reduced market efficiency. In contrast, international markets, such as the European carbon market, have successfully established robust principles to guide market operations. Ref. [142] explored the impact of incentive and constraint policies on rating and certification quality in China’s green bond market, using a two-stage Stackelberg game model to analyze how policy interventions can mitigate issues such as “greenwashing” and inflated ratings. Ref. [143] further compared China’s mechanisms with those of international counterparts, highlighting how economic incentives and clearly defined rules can address inefficiencies and enhance market performance.

• (3). Market dynamics with global best practices to ensure long-term growth.

Existing trading platforms are inefficient and lack user-friendly functionalities, which impedes broader market participation. Ref. [144] proposed integrating blockchain technology to enhance transparency, traceability, and efficiency. Research also designed blockchain-based intelligent trading platforms combined with game-theoretical models to optimize energy trading in microgrids. Through reinforcement learning methods, these platforms simulated customer behaviors, demonstrating significant improvements in load peak-to-average ratios and trading transparency. However, challenges remain regarding the cost of deployment and scalability in a rapidly evolving market like China’s.

• (4). Market entry barriers.

New energy generation enterprises face significant barriers to entry, including complex approval processes and strict qualification requirements, which constrain market diversity and competition. Ref. [145] employing evolutionary game-theoretical models analyzed the strategic interactions among renewable energy producers, traditional coal power plants, and market participants. The findings highlight that optimizing trading strategies and improving transparency can effectively reduce entry barriers and streamline approval processes, thus encouraging greater participation by smaller enterprises.

• (5). Cost uncertainty and sales challenges.

Uncertainty in market scale and trading rules creates higher risks for companies participating in the GEC market. Using Bayesian game-theoretical models, Ref. [146] analyzed the impact of inaccurate renewable energy output forecasts on electricity spot markets, demonstrating that Bayesian–Nash equilibria can effectively optimize bidding strategies for both supply and demand. These findings emphasize the importance of dynamic policy mechanisms that can adapt to changing market conditions and provide a theoretical basis for reducing cost-related uncertainties.

• (6). Lack of international competitiveness.

Domestic green certificates are primarily tied to subsidy programs and are relatively expensive, which limits their attractiveness in international markets. Evolutionary game-theoretical models [147] analyzed the behavior of renewable energy producers under evolving policy frameworks, concluding that aligning with international market quotas and incentives can enhance the acceptance and competitiveness of green certificates. Comparative analyses of global REC markets, such as those in the EU and the United States, indicate that harmonization with international standards significantly improves competitiveness and promotes cross-border trading.

• (7). Environmental benefits and additionality issues.

Ensuring that the renewable energy electricity represented by green certificates is additional is crucial for maintaining market credibility. Ref. [84] using system dynamics models explored the dynamic coupling between carbon trading, green certificates, and electricity markets. These findings reveal complex interdependencies between carbon prices and green certificate values, emphasizing the importance of clear market rules and accounting mechanisms to reduce double counting and enhance environmental additionality. However, the lack of uniform global standards poses challenges to the internationalization of China’s green certificate market.

Looking ahead, with proactive policy guidance, the refinement of relevant laws and regulations, and improved international recognition of green certificates, the development of China’s green certificate market is expected to become more standardized and dynamic. This trajectory aligns with evolutionary market frameworks, and the international influence and acceptance of Chinese green certificates are anticipated to grow. This will create opportunities for Power-Generation Enterprises to participate in international green certificate trading and expand into global markets. Policymakers should draw lessons from international experiences and adapt policies to local market conditions, ensuring the green electricity market realizes its full potential.

6.2. Policy Recommendations

To streamline the green certificate trading mechanism and enhance the overall trading environment for Power-Generation Enterprises (PGEs) [148], several targeted recommendations are proposed to improve both the platform and the mechanisms that govern green certificate markets.

• (1). Strengthening policy incentives and financial support.

Robust government subsidies and financial support mechanisms are essential to enhance green certificate adoption and reduce the overall costs of renewable energy generation. These policies align with global energy transition goals and carbon-reduction commitments under agreements like the Paris Agreement. By reducing financial barriers, subsidies stimulate green energy demand and increase trading volumes of green certificates, allowing electricity suppliers to meet renewable energy targets without directly generating renewable electricity themselves [149].

Subsidies lower entry barriers for producers and consumers, offsetting costs like infrastructure development and operations, which helps PGEs remain competitive against conventional energy producers [91]. They also stabilize renewable electricity prices, making them more attractive to consumers and supporting energy affordability objectives in regions with cost challenges [150].

Targeted subsidy programs can compensate for revenue losses caused by policy-driven price reductions while fostering innovation in areas like battery storage and grid optimization [151,152]. Additional measures, such as tax incentives, further reduce financial burdens and encourage participation in green certificate markets. Subsidies also mitigate investment risks, attracting more capital to renewable energy projects by offering guaranteed returns and reducing uncertainties [153].

In summary, policy incentives and financial support are crucial for growing renewable energy markets. These measures reduce barriers, encourage innovation, and create a sustainable path toward achieving environmental and economic goals.

• (2). Enhancing legal frameworks and strengthening regulatory oversight.

A robust legal framework is essential for maintaining the integrity and transparency of green certificate systems, particularly as energy markets transition toward sustainability. Clear and stringent laws are necessary to address inefficiencies, prevent manipulation, and build trust among participants [18]. Refining existing legal structures is thus critical for the effective governance of green certificate systems.

Defining rights and obligations of market participants: Clearly delineating the roles and responsibilities of stakeholders, such as Power-Generation Enterprises, consumers, and regulatory bodies, ensures access to accurate information and minimizes risks of manipulation or non-compliance. This fosters a transparent and efficient trading environment [11,55].

National-level unified issuance and trading systems: Establishing a unified national platform for green certificate issuance and trading would streamline processes, enhance oversight, and prevent issues like “double-counting” and fraudulent practices [12,154].

Automated monitoring systems: Integrating real-time data analytics and automated compliance systems can enhance transparency and reduce administrative burdens. These tools enable timely detection of violations and ensure swift corrective actions, strengthening market integrity [12,155,156].

Penalizing non-compliance: Effective accountability mechanisms, including financial penalties or restricted market access for violators, can deter fraudulent activities and promote adherence to regulations [157].

Strengthening international alignment: Harmonizing domestic frameworks with international standards facilitates cross-border green certificate trading, enhances global market credibility, and attracts foreign investment [158].

Building public trust: Public awareness campaigns and stakeholder engagement are vital to fostering trust in the system. Clear communication about compliance requirements and consequences of violations strengthens voluntary participation and system effectiveness [159,160].

Future regulatory enhancements should focus on addressing existing legal gaps, leveraging advanced technologies such as blockchain for secure trading, and fostering international cooperation to align green certificate systems globally.

In conclusion, a well-structured legal framework, supported by robust oversight and automation, is key to ensuring the success of green certificate systems. By defining stakeholder roles, establishing unified platforms, and fostering compliance, governments can create a transparent and efficient market to accelerate renewable energy adoption.

• (3). Integrating electricity and carbon markets.

Integrating electricity and carbon markets offers a holistic strategy for aligning renewable energy incentives with carbon-reduction targets, supporting the transition to a low-carbon economy. Establishing joint electricity-carbon markets ensures that the environmental benefits of renewable energy are accurately reflected across both sectors, creating a unified and efficient system.

Development of an integrated electricity-carbon database: A centralized database is essential for tracking energy sources, emissions, and credits, ensuring transparency and avoiding double-counting of environmental benefits. Such a system integrates data from renewable energy sources, grid usage, and carbon trading platforms, offering a unified view of environmental impacts. For instance, Ref. [161] highlighted the importance of real-time carbon emissions monitoring systems for improving market efficiency, while Ref. [162] demonstrated how integrating real-time emissions data into power grids can reduce both emissions and operational costs.

Synergistic trading mechanism: Bundling green certificates with carbon credits creates a unified environmental commodity that satisfies both renewable energy and carbon-reduction goals. This approach simplifies trading processes, increases market liquidity, and minimizes cross-subsidies between policies. As noted by Ref. [163], overlapping policies often reduce efficiency, and bundling mechanisms address these inefficiencies by offering more cohesive market solutions.

Prevention of market distortions: To avoid inefficiencies such as double counting, clear accounting rules must link green certificates and carbon credits. For example, green certificates should be automatically canceled in carbon market accounting systems once used, ensuring their full value is accurately reflected in both markets. As Ref. [164] reveals, double counting can overestimate reductions, underscoring the need for stricter disclosure rules and improved transparency. Regulators must also define clear guidelines to prevent unintended consequences and penalize fraudulent activities effectively.

Reflecting the value of green electricity: Aligning accounting and trading mechanisms across electricity and carbon markets ensures the full environmental value of green electricity is preserved. By integrating these markets and canceling certificates upon use, the integrity of the system is maintained, and the benefits of renewable energy are not overstated.

Integrating electricity and carbon markets presents a significant opportunity to enhance the effectiveness of environmental policies. By establishing centralized databases, bundling mechanisms, and clear accounting rules, policymakers can create a seamless system that promotes renewable energy adoption while reducing greenhouse gas emissions. This approach supports global efforts to transition to a low-carbon economy and maximizes the benefits of both electricity and carbon markets.

• (4). Raising carbon emission-reduction targets and fines.

Strengthening carbon emission-reduction targets and imposing stricter penalties for non-compliance are essential measures to address climate change. These strategies play a vital role in reducing greenhouse gas (GHG) emissions, fostering clean energy innovation, and accelerating the shift toward a low-carbon economy. Policymakers must not only set ambitious reduction targets but also enforce fines that compel companies, particularly in carbon-intensive industries like power generation, to comply with environmental standards and explore alternative energy sources.

Progressively increasing emission-reduction targets ensures continuous pressure on enterprises to innovate and adopt cleaner technologies. This approach signals governments’ commitment to combating climate change, creating a stable policy environment for long-term investment in renewable energy and energy efficiency. Research indicates that stringent carbon limits stimulate technological advancements, as companies strive to meet regulatory requirements while maintaining competitiveness [165]. Additionally, ambitious targets align with international agreements such as the Paris Agreement, embedding domestic policies within a broader global framework of sustainability [166].

Fines play a critical role in ensuring compliance. Without adequate penalties, companies may opt for non-compliance as a cost-effective alternative to adopting cleaner technologies [167]. By aligning fines with carbon market prices, exceeding quotas becomes costlier than purchasing additional allowances, deterring excessive emissions and promoting adherence to regulations. Furthermore, integrating fines with carbon markets increases demand for renewable energy credits and green certificates, further encouraging the transition to cleaner energy sources.

Stricter emission targets and fines also drive technological innovation. Companies facing higher penalties are incentivized to invest in research and development, accelerating the adoption of renewable energy technologies such as wind, solar, and hydropower. Additionally, investments in CCUS technologies become more attractive, helping companies meet stringent emission standards [168].

While punitive measures are essential, supportive policies such as subsidies for clean energy research and tax incentives for exceeding carbon-reduction goals can complement fines. These measures create a balanced approach that encourages compliance while fostering collaboration between governments, industry, and academia.

Raising carbon-reduction targets and fines also supports broader policy objectives, including energy security, environmental sustainability, and economic resilience. By reducing reliance on fossil fuels, these measures enhance energy supply diversification and contribute to improved air quality and public health [169,170]. Moreover, they encourage investment in future-proof technologies less vulnerable to fluctuations in fossil fuel prices, strengthening the resilience of energy markets [171].

In conclusion, raising carbon emission-reduction targets and imposing stringent fines are pivotal for achieving global climate goals and promoting clean energy innovation. These measures drive sustainable market behaviors, encourage technological advancements, and create a pathway toward a resilient low-carbon economy.

• (5). Promoting international certification and global collaboration.

Accelerating the international recognition and certification of domestic green certificates is essential for fostering global cooperation and enhancing competitiveness. Aligning domestic green certificate systems with international green consumption and carbon-reduction programs can facilitate cross-border collaboration and trade. Participation in setting international standards for green certificates would not only boost their credibility but also encourage integrated global efforts toward environmental sustainability.

Promoting international certification harmonizes global environmental policies and broadens renewable energy adoption. Given the interconnected nature of climate change and energy trade, aligning domestic green certificates with international standards strengthens cross-border collaboration and enhances the competitiveness of renewable energy sectors. This ensures the environmental value of renewable energy is recognized globally, minimizes risks of “greenwashing”, and opens international markets for green energy exports. For instance, aligning with the EU’s stringent energy policies can enable countries to export surplus renewable energy while complying with global commitments, enhancing both domestic and international markets.

Aligning green certificates with international frameworks, such as the EU’s ETS and the U.S. REC markets, provides financial incentives for renewable energy producers and strengthens accountability mechanisms for carbon-reduction claims [10]. Such alignment facilitates the trading of green certificates on global platforms, increases market liquidity, and fosters collaboration among nations. Globally recognized green certificates also provide multinational corporations with verifiable tools to meet sustainability goals, encouraging countries to adopt best practices in renewable energy production and integrate these practices into global supply chains.

Active participation in international standard-setting organizations, such as the International Organization for Standardization and the United Nations Framework Convention on Climate Change, is crucial for shaping global energy policies and ensuring that domestic systems remain competitive in the evolving international landscape [172]. Moreover, adhering to international standards can attract foreign investment and encourage the adoption of innovative technologies, further improving the efficiency and competitiveness of renewable energy systems [173].

Beyond fostering global recognition, international certification supports large-scale renewable energy projects, such as offshore wind farms and cross-border solar grids, by ensuring the environmental benefits of these projects are globally acknowledged. It also enhances the value of green certificates in carbon markets by integrating them with carbon-reduction credits, creating a synergistic trading mechanism that prevents double-counting and accurately reflects the environmental value of renewable energy [10].

In summary, promoting international certification for green certificates is vital for achieving global sustainability goals, enhancing market competitiveness, and fostering low-carbon economic growth. By aligning domestic systems with international standards and collaborating in global initiatives, countries can strengthen their renewable energy sectors while contributing to the global transition to a sustainable energy future.

7. Conclusions

As global attention on renewable energy and carbon reduction intensifies, the green certificate market is rapidly expanding, offering significant development opportunities. China, as the world’s largest energy consumer, plays a pivotal role in this market by driving energy structure transformation and pursuing its “dual carbon” goals. The establishment of a green certificate market not only promotes the adoption of renewable energy but also reshapes the market behavior and cost structures of Power-Generation Enterprises, profoundly influencing the competitiveness and pricing mechanisms of the electricity market.

Under new green certificate policies, enterprises—key participants in green certificate transactions—purchase certificates through bilateral negotiations, market listings, or centralized bidding to meet national green energy consumption requirements. As market demand grows and policy incentives increase, the scale of green certificate transactions continues to expand. However, with more participants and greater market liquidity, the complexity of transactions has also risen.

This study explores the strategic behavior and decision-making of Power-Generation Enterprises within the evolving green certificate market. By analyzing the market’s development and its impact on bidding strategies, the study provides actionable insights and recommendations for both policymakers and market participants.

The investigation begins with a review of the current state of the green certificate market, outlining the critical role Power-Generation Enterprises play in green certificate trading. It then applies various game theory models—including Bayesian games, evolutionary games, principal-agent games, and Markov games—to analyze bidding behaviors in the green certificate market. The study further proposes strategies for Power-Generation Enterprises to optimize their cost structures, adapt to dynamic reward and punishment mechanisms, and plan proactively to address market and policy uncertainties.

The key findings demonstrate that game theory is an effective tool for understanding and guiding the strategic choices of Power-Generation Enterprises in the green certificate market. By leveraging these strategies, companies can align their goals with national energy transformation objectives and the “dual carbon” targets. Specifically, companies should focus on optimizing their cost structures, adjusting bidding strategies to seize opportunities, and staying flexible to respond to dynamic market and policy changes. Additionally, by strengthening forward-looking planning, companies can mitigate risks, improve profitability, and maintain a competitive edge while promoting sustainable development.

While the green certificate market presents new opportunities, it also brings challenges, particularly in improving the efficiency of renewable energy generation, reducing costs, and integrating renewable energy into existing electricity markets. Future research should delve deeper into strategy optimization for Power-Generation Enterprises and explore how technological innovation and policy guidance can promote the healthy development of the green certificate market.

Looking ahead, as the green certificate market continues to grow and mature, Power-Generation Enterprises must innovate and adjust their strategies to keep pace with market changes. At the same time, policymakers should strengthen support through targeted incentives and policies, encouraging the widespread adoption of renewable energy and contributing to a global green energy transition.

Author Contributions

Conceptualization, L.C., M.Z., P.H. and W.L.; Methodology, L.C., M.Z., P.H. and W.L.; Formal analysis, L.C.; Investigation, L.C., M.Z., P.H. and W.L.; Writing—original draft preparation, L.C., M.Z., P.H. and W.L.; Writing—review and editing, L.C., M.Z., P.H. and W.L.; Funding acquisition, L.C. and W.L. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are contained within the article.

Acknowledgments

We sincerely thank the associate editor and invited anonymous reviewers for their kind and helpful comments on our paper. The authors wish to acknowledge the use of ChatGPT-4.0, an advanced AI language model developed by OpenAI, for grammar refinement and linguistic enhancement during the preparation of this manuscript. Specifically, ChatGPT-4.0 was employed to identify and correct grammatical errors, improve sentence structure, and ensure consistency and clarity in the presentation of complex scientific concepts. Details of the AI Tool: Tool Name: ChatGPT-4.0; Developer: OpenAI; Purpose of Use: The AI tool was utilized solely for post-drafting linguistic improvements, including grammar corrections, syntax refinement, and enhancement of overall readability. No scientific content, data analysis, or theoretical interpretations were generated or influenced by the AI tool. Access Method: ChatGPT-4.0 was accessed via OpenAI’s official platform and used only for textual improvements. The tool was not applied to data analysis, figure preparation, or any confidential information related to the manuscript. The authors confirm that all scientific concepts, methodologies, and conclusions presented in this manuscript are entirely their original work. The AI tool’s involvement was limited to language-related adjustments and was supervised rigorously by the authors to ensure academic integrity. This disclosure complies with the ethical requirements of the journal and reflects our commitment to transparency in the preparation and submission of scholarly work. We extend our gratitude to OpenAI for providing a valuable tool that facilitated the clarity and professionalism of this manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

Nomenclature

APX TIGRs	APX Tradable Instruments for Global Renewables	GO	Guarantees of Origins
AIB	Association of Issuing Bodies	GC	Green Certificate
ASEP	Asymptotically Stable Equilibrium Point	I-REC	International Renewable Energy Certificates
AUEP	Asymptotically Unstable Equilibrium Point	ISO	Independent System Operator
CCUS	Carbon Capture, Utilization, and Storage	MESS	Multi-population Evolutionary Stabilization Strategy
DPP	Blockchain-based Direct Power-purchase	MARL	Multi-agent Reinforcement Learning,
EM	Electricity Market	MDPs	Markov Decision Processes
EECS	European Energy Certificate System	PGEs	Power-Generation Enterprises
EGT	Evolutionary Game Theory	REC	Renewable Energy Certificate
ESS	Evolutionarily Stable Strategy	RD	Replicator Dynamics
GEC	Green Electricity Certificate (specific to China)	VPP	Virtual Power Plant

Footnotes

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Figures and Tables

Figure 1. Network visualization for the current academic community’s primary research focuses within the fields of energy and electricity markets.

Figure 2. Density visualization for the research on the role of enterprises in the green electricity market.

Figure 3. China green certificate development timeline and policy evolution.

Figure 4. A typical algorithm process to describe the long-term evolutionary game.

Figure 5. The dynamic adjustment process of pure pricing strategies is proposed by Cheng and Yu (2018) for investigating two categories of Power-Generation Enterprise groups. (a) Strategy combinations at asymptotically stable equilibrium points (ASEPs): Illustrates the two stable strategy profiles where both types of Power-Generation Enterprises adopt either the base-price bidding strategy (0, 0) or the high-price bidding strategy (1, 1). (b) Influence of payoff parameter variation on saddle point position: Demonstrates how changes in the payoff distribution parameters shift the location of the green saddle point (xs, ys) within the decision region [0, 1] × [0, 1]. (c) Alteration of convergence domain SL1 with saddle point shifts: Shows the modification in the size and distribution of the convergence domain SL1 as the saddle point moves due to varying payoff parameters. (d) Alteration of convergence domain SL2 with saddle point shifts: Depicts the changes in the size and distribution of the convergence domain SL2 in response to shifts in the saddle point position caused by variations in payoff parameters. The region ①, bounded by the origin (0, 0), (0, 1) and the saddle point (xs, ys), and the region ②, bounded by the origin (0, 0), (1, 0) and the saddle point (xs, ys), both represent that the initial states within the two domains are directed towards converging to the base-price bidding strategy equilibrium (0, 0), indicating that the system evolves towards a stable and competitive market condition characterized by reasonable pricing. The region ③, bounded by the origin (0, 1), (1, 1) and the saddle point (xs, ys), and the region ④, bounded by the origin (1, 0), (1, 1) and the saddle point (xs, ys), both represent that the initial states within the two domains are directed towards converging to the high-price bidding strategy equilibrium (1, 1), indicating that the system evolves towards a less competitive market condition characterized by elevated pricing levels.

Figure 6. The advantages and features of the application when using Evolutionary Game Theory to study multi-group behavioral decision-making issues.

Figure 7. Simulation results for Stackelberg game-based decision-making in a green certificate electricity market, focusing on leader-follower interactions, payoff dynamics, and strategy convergence. (a) shows the final-day payoff distribution between the leader and the followers. (b) demonstrates the three-dimensional trajectory of the simulation, encompassing day count, leader strategy x, and mean follower strategy [Forumla omitted. See PDF.]. (c) displays a heat map of the followers’ strategic evolution over time, highlighting the spatiotemporal variations in y. (d) illustrates the progression of both the leader’s strategy x(t) and individual follower strategies over the 365-day horizon. (e) shows the time evolution of the leader’s payoff and the mean follower payoff, thereby underscoring their mutual adaptation and convergence. (f) presents a three-dimensional scatter of followers’ strategies versus their payoffs and follower indices at the final day, providing insight into the distribution of outcomes under the Stackelberg equilibrium.

Figure 8. A typical algorithm process to the Markov game.

Figure 9. A multi-agent reinforcement learning system.

Figure 10. The application of Markov games in the decision-making process of Power-Generation Enterprises in the electricity market bidding within a multi-agent system.

Figure 11. Green certificate issuance transaction process.

Figure 12. The relationship between Power-Generation Enterprises and the electricity market and green certificate market. Blue Arrows: Represent the interactions and feedback loops within the electricity market. These include the relationships between electricity supply, demand, price, and government policies. The blue arrows illustrate how traditional factors like market dynamics (electricity demand and supply) and policies influence the overall energy system. Green Arrows: Highlight the mechanisms related to the green certificate market. These arrows specifically emphasize how green certificate demand and pricing interact with new energy power generation enterprises, influencing investments in renewable infrastructure and the purchasing/selling of green certificates. They demonstrate the financial incentives for promoting green energy. Black Arrows: Indicate the direct actions or consequences that link government subsidies, penalties, and investments. These arrows represent how governmental policies directly impact both traditional and new energy power generation enterprises, driving compliance and the transition toward greener technologies.

Table 1

Cross-regional comparison of renewable energy certificate types and market characteristics.

Renewable Energy Certificate Type	Region	Issuing Organization	Recognition Level	Supported Project Types
APX TIGRS	USA	APX (non-profit)	RE100 recognized	Non-subsidized renewable energy projects
I-REC	Global	I-REC Foundation	RE100 recognized	Initially state-owned enterprise projects, later expanded to include non-state-owned projects
GEC	China	National Energy Administration	Domestically recognized, conditionally recognized by RE100	Concentrated wind or photovoltaic projects, both subsidized and non-subsidized
GO	Europe	Various issuers	Varies	Various renewable energy projects, typically including both subsidized and non-subsidized

Table 2

Comparison of game-theoretical methods.

Comparison of Game Methods	Classical Game Theory	Evolutionary Game Theory	Hierarchical Game Theory	Bayesian Game Theory	Markov Game Theory	Deep Reinforcement Learning Based Game
Game Assumptions	Rational participants	Limited rationality of participants	Leader and follower	Complete information	Intelligent agents with memory	Intelligent agents improve strategies through learning
Game Forms	Individual or group	Group	Leader and follower	Individual	Individual or group	Group
Game Equilibrium	Nash Equilibrium (NE)	Evolutionary Stable Equilibrium (ESE)	Hierarchical equilibrium	Bayesian Nash Equilibrium	Markov Decision Process (MDP) equilibrium	Strategies are optimized through neural networks
Game Process	Static or dynamic	Dynamic	Dynamic sequence	Static	Dynamic	Dynamic
Conditions for Game Equilibrium	Iterative strategy or retaliatory strategy	Evolutionary selection through group members	Leader decides first, follower adjusts based on leader’s decision	Bayesian updates	Bellman equation	Deep learning algorithms
Representative Games	Prisoner’s Dilemma, Chicken Game	Flocking foraging, Evolutionary stable strategies	Price leadership models	Signaling games in electricity market bidding	Electricity market bidding	AlphaGo, Atari games, Technology adoption

Table 7

Comparison of game-theoretical methods in aspects of advantages and disadvantages.

Game Types	Advantages	Disadvantages
Bayesian Game	Models decision-making with incomplete information; reveals strategic interactions under uncertainty.	Complex equilibrium solutions; assumes rationality and common knowledge.
Evolutionary Game Theory	Adapts to dynamic environments; accounts for non-rational behavior and genetic strategy selection.	Slow convergence to stable strategies; high computational demand for simulation.
Stackelberg Game	Defines clear leader-follower dynamics; suitable for markets with asymmetric control.	Limits strategic flexibility for followers; may not capture market complexities fully.
Markov Game	Manages stochastic elements; ideal for Intensive computational requirements; sensitivity to initial strategy configurations.	High state space complexity; requires precise transition probabilities.
Deep Reinforcement Learning Game	Neural network-driven strategy optimization; adept at handling complex, high-dimensional decision spaces.	Intensive computational requirements; sensitivity to initial strategy configurations.

Table 8

Scenario analysis of power suppliers’ strategies and revenue dynamics under varying RPS implementation intensities.

Policy Intervention Scenarios	Corporate Strategies	Revenue Impact	Strategy Evolution Pathway	Stability
Slow development scenario (weak RPS enforcement)	Both coal-fired and green power companies abstain from trading	Maximum revenue but no trading activities	Remains stable with “no trading”	High, with minimal market fluctuations but low trading activity
Moderate development scenario (moderate RPS enforcement)	Coal-fired companies purchase green certificates, while green power companies abstain from selling	Balanced revenue, with additional income from certificate trading	Coal-fired companies shift from “wait-and-see” to “buying certificates”, while green power companies remain passive	Moderate, as green power companies do not participate, limiting market competition
Rapid development scenario (strong RPS enforcement)	Coal-fired companies purchase green certificates, and green power companies sell certificates	Significant revenue growth through high-intensity certificate trading	Coal-fired companies move from “wait-and-see” to “high trading volume”, while green power companies shift from “low trading volume” to “high trading volume”	High, with active trading, intense competition, but higher technical requirements

Table 9

Implementation outcomes of government policy tools under policy interventions.

Policy Interventions	Policy Actions	Revenue Impact	Evolution Pathway	Stability
Carbon pricing mechanism	Implement Carbon Tax	Increases fiscal revenue while reducing high emissions; may raise corporate costs, limiting mitigation incentives.	Transition from “high emissions and high tax” to “low emissions and low tax” as firms adapt.	High, but excessively high carbon prices risk firm withdrawal or backlash.
Stricter renewable energy targets	Increase Subsidies and Regulation	Higher fiscal spending accelerates renewable energy adoption and target achievement.	Shift from “low renewable share” to “high renewable share” driven by strong policy incentives.	High, suitable for long-term energy planning; fiscal pressure must be carefully managed.
Electricity market reform	Implement Time-of-Use and Market-Based Pricing	Reduces fiscal burden while improving market efficiency; requires high adaptability from firms and users.	Transition from “fixed pricing” to “market-based pricing” with faster behavioral adjustments.	Moderate to high, short-term volatility may affect policy outcomes.
Mandatory GC quotas	Enforce GC Trading Proportions	Short-term volatility increases but green electricity share improves under quota pressure, ensuring target achievement.	Transition from “low GC adoption” to “high GC adoption”, stabilizing the GC market over time.	High, though GC price fluctuations could affect market confidence.

Table 10

Behavioral adjustments and demand responses of electricity users under market mechanisms.

Market Mechanisms	User Behavior	Revenue Impact	Evolution Pathway	Stability
Time-of-use pricing implementation	Adjust Electricity Usage Timing	Users shift consumption to low-price periods, significantly reducing overall costs.	Transition from fixed to time-shifted consumption, adapting to price signals.	High, but requires long-term market education; some users may lack price sensitivity.
Green certificate cost pass-through	Increase Green Electricity Consumption	Slightly higher costs with increased green electricity adoption and enhanced environmental awareness.	Transition from low to high green electricity consumption as user acceptance improves.	Moderate, with potential dissatisfaction from high costs, but long-term adjustments trend positively.
Carbon tax indirectly impacting prices	Reduce High-Energy Consumption	Increased costs for high-energy users, reducing demand while boosting green electricity consumption and environmental awareness.	Transition from high-energy to low-energy demand as users adapt to carbon tax pressures.	High, though excessively high carbon tax rates may trigger rebound effects or reduced consumption.
Dynamic price adjustment	Optimize Electricity Usage	Short-term price fluctuations drive structural adjustments, improving alignment with green electricity supply.	Transition from passive to actively managed consumption, rapidly increasing green electricity share.	Highest, suitable for mature markets with well-established dynamic pricing frameworks.

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