Modeling and Prediction of Sustainable Urban Mobility Using Game Theory Multiagent and the Golden Template Algorithm

Abstract

The current development of multimodal transport networks focuses on the realization of intelligent transport systems (ITS) to manage the prediction of traffic congestion and urban mobility of vehicles and passengers so that alternative routes can be recommended for transport, especially the use of public passenger transport, to achieve sustainable transport. In the article, we propose an algorithm and a methodology for solving multidimensional traffic congestion objectives, especially for intersections, based on combining machine learning with the templates method—the golden template algorithm with the multiagent game theory. Intersections are modeled as independent players who had to reach an agreement using Nash negotiation. The obtained results showed that the Nash negotiation with multiagents and the golden template modeling have superior results to the model predictive control (MPC) algorithm, improving travel time, the length of traffic queues, the efficiency of travel flows in an unknown and dynamic environment, and the coordination of the agents’ actions and decision making. The proposed algorithm can be used in planning public passenger transport on alternative routes and in ITS management decision making.

1. Introduction

In recent years, there has been a growing interest in using game theory algorithms implemented with intelligent agents to develop software systems to assist decision making and agent-based management systems. Prediction and decision-making theory is based on mathematical algorithms for making decisions and generating strategies that can be applied if the results of potential actions are unknown. The game theory was developed long before the concept of “smart agent”. Agents are examples of software applicability for decision makers who can combine the classical decision-making theory with artificial intelligence algorithms.

In general, decision/prediction theory analyzes and needs to choose a predefined scenario when the result is unknown after choosing a working system. Decision theory focuses on identifying the best decision, accepting that the concept of “the best” can have several meanings. The most used decision is to maximize the final planning result that the decision maker proposes.

Game theory studies how interaction strategies between individuals can be developed to maximize an agent’s well-being in a multiagent interaction and how the decision maker can impose protocols or mechanisms of interaction with properties. It can be noticed that the theory of decision is considered the study of game theory (survival) against nature, where nature (environment) is an opponent who does not want to obtain the best compensation because he has a chaotic behavior. Therefore, many applications based on game theory, implemented on multiagent systems (experts), have been developed to analyze events such as negotiation and coordination/planning.

The concept of decision prediction has evolved from the concept introduced by Michael S Scott Morton [1] to the decision management system based on intelligent agents. Sprague [2] defined decision support system (DSS) as “interactive computer-based systems that will help decision-making management use data and predictive models to solve problems”. This definition was proactive, so it was generalized to include all systems involved in prediction and decision making [3,4,5,6]. The extension of the initial definition led to hiding under the name of DSS of different types of systems, many of them having nothing to do with the initial idea of DSS. Initially, these were tools aimed at large companies, but in recent years, DSSs have become essential and accessible tools for small companies. The existence of these tools has changed and will continue to change the way we make decisions. They allow the individual or organizational decision maker to manage information volume and complexity more efficiently and better coordinate activities.

In most cases, DSSs are developed and implemented in companies in all activity fields. Although most companies have hierarchical leadership, decision making is a collective process. The decision-making group can be involved in making the decision. Still, the decision can also be caused by a single person, such as creating a short list of alternatives or choosing the criteria for accepting an option. The primary purpose of the DSS system is to use appropriate mechanisms (analysis of data, documents or calculations, and predictions) to support making the right decision for a situation imposed by certain situations [7,8,9]. The correct decision can be taken, only after a careful analysis of all possible results obtained, considering all the factors that may influence the decision-making act and following the research performed by all parties involved in the management process.

The decision results from the analysis of choosing an optimal action direction often involve allocating new resources. The prediction obtained from processing information and databases, which may belong to a person or a group of people with the necessary authority, is ultimately used by decision makers in particular concrete situations [10,11,12,13]. A complex decision-making environment creates the essential framework for using decision-making software applications. Research and case studies analyzed by us have shown that a well-designed and structured IT system to support decision making can improve the quality of managerial decisions and increase the efficiency and effectiveness of the management process.

Today, computer systems have become a powerful tool to help in decision-making. Decision makers work better with the relevant information obtained in the shortest time. Effective support decisions can give managers greater independence in retrieving and analyzing data (big data), thus securing quality information and desired results. The decision-making process can take place based on a well-defined scenario, which can be formulated tangentially with the rules of a game in the concept of game theory (depending on the field of applicability) through the following stages:

• •. Identifying all parties involved in the decision-making process (persons or groups of persons);

• •. Defining the possible actions (scenarios) each party participating in the given process can undertake;

• •. Establishing the evaluation process’s rules (evaluation stages and existing priorities);

• •. Establishing the criteria according to which the assessment will be made, and the respective decision will be adopted;

• •. Creating a list of alternatives and choosing the criteria for a predictive alternative;

• •. Creating compromises and balancing interests or creating coalitions in case of need (imposing these compromises if necessary);

• •. Distributing results according to the defined criteria (directing the gains according to the adopted decision).

Given an individual scenario of negotiation between agents (decision makers), various techniques in the field of game theory can be applied, which refer specifically to the definition of the protocol rules of negotiation. Protocols can certainly have predefined (default) properties:

• •. Guaranteed success;

• •. They are maximizing social status;

• •. Efficient wall;

• •. Individual choice;

• •. Stability of choice;

• •. Simplicity of the solution;

• •. Distribution of the decision.

Among the most critical aspects that must be highlighted during the design stage of DSS is the establishment of the user and the beneficiaries for whom the respective system will be destined, as well as the fields of use and the way of functioning it. Regardless of whether a single person or a group of people will participate in the decision process, systems must satisfy the essential characteristic, which consists of “providing support and improving the way of human judgment, control of the system, the system thus remaining entirely under the control of the user” [14,15,16,17].

Thus, Bagagiolo and Bauso [18] define five categories of roles of people involved in the process of design (construction) and use of DSSs, considering the classification of DSSs in terms of technological levels (specific DSSs, DSS generators, DSS tools):

• •. Managers/decision makers (users)—the person who makes the decision and will be responsible for the consequences of the choice.

• •. Intermediaries—the person who helps, to a certain extent, the manager use the support system for specific decisions and in choosing the decision by providing suggestions.

• •. DSS builder/facilitator—the person who designs and builds/configures the specific DSS using a DSS generator. The builder must know both the field of decision making and technical knowledge.

• •. Technical support staff—the person develops new features for DSS as parts of the DSS generator (databases, analysis models, new presentation elements).

• •. DSS instrument developer—the person develops new technologies, languages, hardware, and software components to improve subsystem connections.

According to several studies [19,20,21], a person can assume one or more roles depending on the nature of the problems, the level of technical academic background, and the person’s orientation. Other studies regroup these roles into three categories [22,23]:

• •. Users are all those in direct or mediated interaction with DSS to form a decision-making unit in elaborating and adopting decisions.

• •. Intermediaries connect users and developers of DSS instruments in the transition from tools to customized systems (builders–specialists) or mediate and even facilitate application systems.

• •. DSS tool makers are specialists who develop decision-making methods and those who implement associated IT products, including DSS generators.

In recent years, different solutions for planning personalized trips (vehicles, trains, passengers) have been researched and developed within the intelligent transport systems (ITS). In Zambrano-Martinez et al. [24], the k-means technique generates the clusters, followed by a principal component analysis to extract the main clustering features that enable visual representation. In Kerner et al. [25], the modeling is performed through travel time curves, digital maps, and routing software for traffic prediction.

Another research presented by Min and Wynter [26] develops a methodology to predict traffic based on time series. Costa et al. [27] described the components of a big data traffic architecture for analyzing and predicting road traffic at a macro level. Some studies dealing with traffic prediction involve learning algorithms, such as fuzzy logic [28], although facing problems, such as low accuracy and efficiency. For instance, Onieva et al. [29] presented a case study in which an automated vehicle must cooperate with a driver to achieve cross-road maneuvers without risk and developed a three-layer hierarchical fuzzy-rule-based system. Hodge et al. presented a neural network algorithm for short-term traffic flow prediction using univariate and multivariate data from a single traffic sensor [30]. Habtie et al. [31] developed a study to estimate the state of road traffic using the cellular network as a source of traffic data and used a model for evaluating the state of the neural network. Other authors trained a set of hidden Markov corresponding to five traffic patterns [11,22,32].

The best example is planning a trip through the personalized choice of the destination (trip’s beginning and end), the means of transport, and possibly information about the route so that it is adaptive using game theory [33,34]. This adaptive planning can lead to changing the behavior of travelers regarding urban mobility and achieving sustainable transport, a very complex problem. In the Cococcioni et al. research [35], an advanced system for travel information was proposed, and Sedjelmaci et al. [36] proposed a multiagent route management system. In both references, the data used are only about traffic conditions, considering the mobility of travelers for the use of multimodal/multidimensional trips.

Another applicability of ITS using game theory is the prediction of traffic congestion to determine whether travelers use public transport more to the detriment of personal vehicles. This aspect is sustainable, primarily if the authorities use subsidies for public transport and additional taxes for traffic congestion applied to traffic participants. Thus, multiagent architectures and game theory can be successfully used for independent or cooperative processes to manage traffic congestion. The game theory algorithm was also successfully used for traffic light management [37].

The article proposes a multidimensional traffic congestion prediction algorithm for urban intersections using the golden template algorithm for intersection modeling and multiagent game theory. The traffic flows entering the intersections are modeled as independent players who must finally reach an agreement. To achieve the agreement between independent players, we use Nash negotiation. To evaluate the proposed algorithm, we compared the obtained simulations with the traditional model predictive control (MPC) algorithm, currently used for ITS traffic prediction. The results showed that the multiagent Nash negotiation applied to intersection modeling with the golden template algorithm outperforms the MPC algorithm, improving the travel time, the length of traffic queues, the efficiency of travel flows in an unknown and dynamic environment, and the coordination of the agents’ actions and decision making.

The paper proposes an ITS traffic prediction analysis to find the best solutions for solving multidimensional traffic congestion objectives, especially for intersections based on multiagent game theory, using the golden template algorithm for modeling intersections. The rest of the paper is organized as follows: Section 2 presents an introduction to ITS issues and materials and methods used to profile a methodology for traffic management; Section 3 presents the results obtained with IMAS; and finally, conclusions are presented in Section 5.

2. Materials and Methods

2.1. Game Theory and Decision Making

The classical game theory models have found their applicability during the last decades in different social fields to analyze problems with decision-making or conflicting character. The most common are applied to issues in economics, management, or marketing, but also in sociopolitical difficulties of a voting nature. They apply to various social methods in which there is usually no independent fake choice that one can make—in which the best results depend on the actions of the other participants [38,39]. In game theory, the consequences refer to the values each participant receives due to his choices and his opponent’s activity. Numerical values often represent the consequences; these numerical values can be represented discreetly—matrix or continuously. A key concept in game theory is the criterion of optimality. It refers to the rational decision in which a setup of movements is designated to bring an optimal reward, even after evaluating all possible actions of appearances. In game theory, the concept of the game solution of two or more people means a situation of balance for all players. The crucial issue is adapting the classic mosquitoes from game theory to various decision-making problems in different social, economic, and political fields. Simultaneously choosing the appropriate model for the issue in question, it is essential to determine the solution and the correct interpretation in the respective area.

2.2. Development of Intelligent Transportation Systems Based on Artificial Intelligence Algorithms

Intelligent transport systems are electronics, IT, and communications applications in the transport field. Their primary objectives are to reduce the harmful effects of transport activity (accidents, material losses, additional costs, pollution) and increase the efficiency of this activity. Intelligent transportation systems (ITS) originated in the United States and were initially used in road transportation to define traffic lights and traffic management equipment and facilities [40,41]. “Intelligence” at that time was given using electronics in the transport field and was more a term imposed by marketing and not a term set by technology. Many ITS applications now use solutions based on artificial intelligence (AI), data mining, big data, and so-called innovative technologies. Therefore, this means that intelligent transport systems are defined by the used technologies and not by marketing tools.

Figure 1 shows a diagram of ITS management and control services and modules that can be integrated using artificial intelligence algorithms. The traffic control, incident manager, and traffic request management modules can be modeled using Machine Learning with Templates (golden template algorithm) for situation recognition and predictive modeling, advanced software components for ITS architectures, proposed in this article. Based on the incident management predictions, it is possible to use the electronic payment management mode required by insurance companies that must pay road accident damages [42].

Figure 2 shows the modules of the ITS architecture composition and the AI algorithms used to implement them. According to Figure 2, the most used artificial intelligence algorithms are artificial neural networks (ANN), genetic algorithm (GA), fuzzy logic (FL), and evolution strategy (ES).

2.3. Multiagent Systems Theory

This subsection will introduce multiagent systems formed by several interconnected agents. Multiagent systems represent the ideal means to approach problems with several methods of solving, structuring, and entities that solve them (as in the case of distributed systems). Such systems have, therefore, the natural advantage of distributed and concurrent problem solving, but at the same time, they also have the additional benefit of representing complex modes of interaction. The main types of interactions are cooperation (working together to achieve a common goal), coordination (organizing problem-solving activity so that harmful interactions are eliminated and favorable ones are used), and negotiation (reaching an agreement that is acceptable to all parties involved), which represent essential aspects of the practical use of agent-based methods [43,44].

The notion of the agent in a broad sense is used for a computational system (entity) with the following properties:

• •. Autonomy: the agent operates without the direct intervention of people or other methods and has specific control over its actions (activities) and internal state.

• •. Reactivity: the agent perceives the surrounding environment (which can be a physical reality, a user through a graphical interface, a lot of other agents, the Internet or Intranet, or a combination of them) and responds in a certain way to continuous changes and unforeseen events that occur in the environment.

• •. Proactivity: the agent does not react only in response to changes in the environment; he can have behaviors oriented towards achieving some goals, having his initiative in this sense.

• •. Social ability: the agent interacts with other agents (and possibly humans) using a specific communication language understood by all other agents (or humans).

A fundamental problem in intelligent multiagent systems (IMAS) is the cooperation between agents, which may be heterogeneous, to achieve common objectives. Suppose in the case of single-agent systems, planning could build a sequence of actions starting only from goals, resources, and environmental restrictions [45,46]. In that case, IMAS planning requires considering the role of another agent’s activities in the choice by a particular agent of his action strategy. In the initial systems, in which groups of agents pursued common goals, interactions between agents were determined by cooperative strategies constructed to improve their collective performance, hence the need for complete planning before action. To produce a coherent plan, agents had to recognize interactions between subgoals and eliminate or resolve them.

This proposed architecture solves this problem by including a synchronizer agent that recognizes and resolves such interactions in an architecture proposed in this article. The other agents send their plans to the synchronizer; it examines methods for critical regimes where, for example, resource availability may cause agents not to fulfill them. The synchronizing agent inserts synchronization messages that function as semaphores to ensure mutual exclusion and thus avoid collision between agents in fulfilling their plans.

Another way of approaching cooperation in IMAS was oriented towards the “work team” concept. Applicable, especially in a dynamic environment, the method assumes that the agents in IMAS form a team that can make mistakes or has new opportunities in fulfilling the established tasks. Each team member is monitored for performance, and the team is reorganized according to the current situation.

2.4. Negotiation and Learning in Intelligent Multiagent Systems

If the agents in an intelligent IMAS are self-interested (so they also pursue their own goals), then the focus falls on negotiation. Negotiation is a method of coordination and conflict resolution between agents. Such conflicts can appear in planning activities and tasks, solving the problems of allocating critical resources, and solving the inconsistency between functions and activities in determining the organizational structure. Negotiation is necessary for communicating the change of plans, the allocation of tasks, or the centralized resolution of violating restrictions.

The main characteristics of a negotiation process in IMAS are:

• (a). The presence of a particular form of conflict that must be resolved in a decentralized manner;

• (b). The existence in IMAS of some self-interested agents (who also have their own goals) or selfish agents (who only have their purposes);

• (c). Bounded rationality so that the agents can make rational decisions independently but within certain limits;

• (d). Incomplete information;

• (e). Communication between agents.

The learning method proposed in this article is based on game theory. Each agent has an associated utility function, and the values of this function are represented in a payoff matrix known to both agents included in the negotiation. Each agent also appreciates an alternative law that will maximize their utility. Although the method based on game theory is simple and elegant, it has restrictive solid assumptions that make it challenging to apply to practical situations. Negotiations in the real world occur under partial or complete uncertainty, including multiple criteria that cannot be synthesized only by a utility function. Agents’ utilities are not known, so agents are not omniscient.

Another essential aspect in the negotiation between self-interested agents is the ability to adapt their behavior to changing circumstances. This aspect is related to the learning process. Learning in intelligent IMAS is challenging to address since, as the other agents know, the agent’s environment changes, such as ITS dynamics. In addition, the actions of the other agents may be unobservable, so the learning agent may make significant errors regarding the new behaviors it will encounter.

Starting from these considerations, we propose the concept of conjectural equilibrium, defined as the situation in which all the expectations of the agents regarding the behaviors of the other agents are realized, and each agent responds optimally to their expectations. In this type of IMAS, each agent builds a model of the other agents’ responses to its behavioral changes because of learning. In a tested negotiation model for ITS, called the bazaar model, learning is performed through interactions between agents, so it is an ongoing process as IMAS operates [47]. The study of this negotiation and learning model essentially showed that:

• (a). When all agents learn, the utility of the entire system is close to optimal, and the utilities of individual agents are similar.

• (b). When no agent learns, the utilities of the individual agents are almost equal, but the utility of the entire system is shallow.

• (c). When only one agent learns, his utility increases, but the utility of other agents and the system’s overall utility decrease.

3. Results

3.1. Game Theory and Intelligent Multiagent in Urban Transportation Planning

The proposed method is based on implementing game theory and intelligent multiagent systems (IMAS). Each agent has an associated utility function, and the values of this function are represented in a payment matrix known by both agents included in the negotiation. Each agent also appreciates an alternative law that will maximize its usefulness. Although the method based on game theory is simple and elegant, it has exceptionally restrictive assumptions that make it challenging to apply to practical situations. Real-world negotiations occur in conditions of partial or complete uncertainty, including multiple criteria that cannot be synthesized by a utility function alone. The agent’s utility is unknown, so agents are not omniscient (all-knowing). Another way to allow an agent to learn and use an evolutionary algorithm is by using biology, deriving from the theory of evolution through natural selection.

It works with a population of individuals, each with a certain measurable fitness level, using a metric defined by the model builder.

Evolutionary game theory and population dynamics are based on the approaches proposed by Sandholm [48] and Smith [49].

Consider a population composed of a large and finite number of rational decision makers (agents). All the decision makers can select among a set of strategies denoted by $\mathsf{{\rm Y}}=\left\{1,\dots ,n\right\}$, which represent the actions that the agents can take. The scalar $x_i\in {ℛ}_{+}$ represents the portion of decision makers selecting the strategy $i\in \mathsf{{\rm Y}}$. The vector $x={\left[x_1\dots ..x_n\right]}^{⊺}\in {ℛ}_{+}^n$ is the population state or strategic distribution whose entries are non-negative real numbers. A possible state set is:

(1)$X=\left\{x\in {ℛ}_{+}^n:{\displaystyle \sum }_{i\in \mathsf{{\rm Y}}}{x}_i=m\right\}$

where m > 0 is the population mass.

Agents playing the i-th strategy obtain a reward from a fitness function denoted by $F_i\left(x\right)$, where $F_i:X\to ℛ$ is a continuous map specifying the payoff associated with the strategy $i\in \mathsf{{\rm Y}}$. The fitness function vector completely characterizes the population game, Nash equilibrium of F, $F\left(x\right)={\left[F_1\left(x\right)\dots \dots F_n\left(x\right)\right]}^{⊺}$.

Figure 3 represents a simulation of selecting the bus destination using game theory. The simulation is performed in the LabVIEW graphical programming language, produced by National Instruments, Austin, TX, USA, version 2020.

The most representative individuals are reproduced by multiplying with others adapted to the process, by multiplying them, resulting in descendants who have characteristics taken from both parents. Multiplication continues over several generations, leading to a state of mobility as the population evolves and adapts to the environment. In the case of neural networks and genetic algorithms, the software developer must decide on the conditions imposed on the development model. For example, in the case of models based on genetic algorithms, a single agent can represent the entire population. The genetic algorithm will become a black box used by the agent for learning and adaptation to the environmental conditions imposed by the developer. Alternatively, everyone can be programmed as an individual agent, and the result obtained will be a population of intelligent agents interpreted in the process of evolution. Similarly, we can program each agent or group of agents with neural networks, and each development environment (economy) and society to be represented as a single neural network, each neuron being assimilated with an agent (for this situation, it is not easy to build all the attributes of the agent).

3.2. Implementation of the Intelligent Multiagent Systems Algorithm for Urban Transport Planning

One of the simplest but most effective ways to develop agent-based models is to use a production system algorithm. A production system algorithm has three components:

• •. Multiple rules;

• •. Dynamic working memory;

• •. A set of prediction rules.

The established rules have two fundamental parts: conditions that specify when the imposed regulations will be enforced and when the planned actions will be carried out.

For example, an agent may be designed to walk in a simulated environment to purchase any food he encounters in action. Such an agent will work according to the rule: If I come across a food WHEN I buy it. This would be one of the rules, and each direction in the instruction set will have a different condition. Some rules may include actions that present facts in the agent community’s collective memory, and the conditioning rules will test the collective memory [50,51]. The set (database) of rules analyzes each direction, chooses the regulations for which most conditions are met, and performs the specified actions, repeating this cycle an unlimited number of times. Different rules can be executed for each action cycle because the environment changes after an enforced rule changes the collective memory so that new rules for the population’s functioning are generated. Using a production system algorithm is easy to build and introduce intelligent reactive agents that respond to external environmental stimuli through actions in the community. It is also possible, but more challenging to achieve agents who may have the ability to think (reflect) on the movement of the environment and the decisions made to shape their knowledge. Another possibility for development is to build agents who create rules (learn independently) using an adaptive algorithm that favors practical actions and can sanction other population members. This kind of development represents the basis of classification and decision systems.

3.3. Formation Simulations with Projection Dynamics

It follows a LabVIEW simulation that performs the distributed control problem with the particular task of obtaining a triangular formation using an adaptive algorithm based on an intelligent multiagent with game theory.

Figure 4 shows how the coordinates converge to the final desired values. Finally, in Figure 5, the trajectories of the agents are represented, and the triangular formation they perform is highlighted.

Agents designed based on the production algorithm have a high potential to adapt and analyze their environment. They can also develop new rules, adding knowledge to the population’s collective memory (action memory). To solve specific problems is necessary to create intelligent agents capable of learning independently so that the internal structure and processing of the rules constantly adapt to the dynamic environmental conditions. To achieve the requirements for adapting agents to the environment, they can be developed on the principle of functioning neural networks because they are closest to the human thinking mechanism.

In this context, the designed cognitive architecture of an agent can be defined as the part of the system that provides and manages the agent’s primitive resources. Cognitive architectures usually fold on an information cycle that begins with receiving information by monitoring the execution environment, continuously filtering and processing them, memorizing relevant knowledge, deciding based on the current status and previous experience, and ultimately taking action [52,53]. A system that implements such an architecture should be able to perform a diverse range of cognitive tasks, using several problem-solving and information representation methods, and learn as many aspects of work tasks as possible and the success of their fulfillment. Theoretically, with an architecture for general intelligence, any part of intelligence would be studied, and the system should be able to model it within the considered structure.

We developed an application for traffic modeling in an intersection based on game theory implemented with an intelligent multiagent. The simulation was carried out on the architecture and distant horizons using the historical traffic data to predict the smoothing of the traffic through the automatic modification of the traffic lights.

Figure 6 shows some sequences from the traffic modeling of an intersection based on game theory implemented with an intelligent multiagent.

In the academic and research activity, a simulator was developed using the Matlab environment capable of simulating simple traffic scenarios with vehicles and intersection controllers. The simulator provides simulation models for road networks, populating them with vehicles and specifying trajectories for vehicles and traffic lights. It is designed so that users can set their logic control for both vehicles and traffic signals. The simulator aims to test multiagent autonomous vehicle control algorithms and intelligent traffic control algorithms. The simulator also has functionality by simulating traffic in a closed loop, where the speed trajectories of the vehicles are not given a priori but are the product of state-dependent control logic. The traffic simulator was parameterized with the following parameters:

• -. Representing the network as a directed graph of connected lanes and turns that vehicles can use to specify their routes through the network;

• -. Mapping between global position, station distance along the length of the strip, and direction and curvature of the strip;

• -. Connecting vehicles and traffic controllers;

• -. The driving strategy module that controls the vehicles in the network (i.e., it does not assume any lane-keeping dynamics);

• -. Car tracking models.

Figure 6 shows sequences from traffic modeling through intersections using the developed simulator. The algorithm used for the driving strategy uses multiagent game theory, and the traffic through the intersection is modeled with the golden template algorithm (Machine Learning with Templates).

Based on the prediction model from Figure 6, we implemented a real-time modeling application of traffic light times (traffic flow detection at intersections) based on artificial intelligence algorithms. New machine learning methods and knowledge representation have sought to provide superior technology applications. In this regard, Machine Learning with Templates pertains to recognizing categories and predictive modeling, which can be essential components of advanced software technology. Machine Learning with Templates was designed to use the advantages of bottom–up and top–down methods. Over the last few decades, some AI practitioners in cognitive psychology, machine learning, game theory, and neurobiology have observed that some cognitive tasks are better suited to bottom–up methods, while top–down methods better perform other tasks. Machine Learning with Templates is flexible enough to create useful applications in bioinformatics, financial data mining, goal-based planners, handwriting recognition, information retrieval, multiagent intelligence, natural language processing/understanding, and voice recognition.

A probabilistic machine learning algorithm scales favorably to enormous datasets, avoids local minimum problems, and provides fast learning and recognition speeds. Templates may be created using the golden template algorithm made here or game theory and evolutionary algorithm or synthesized using a combination of these methods. Each template has a prototype and matching function, which can help improve generalization. Figure 7 shows the mathematical modeling of the intersection for traffic detection using Machine Learning with Templates (golden template algorithms).

The following Figure 8 presents the results of real-time video analysis for traffic flow detection using machine learning with templates.

4. Discussion

The evolution of information technologies has led to the emergence of technical systems that fundamentally change how people live and even offer new models of economic activities. Intelligent systems can generate inferences based on embedded or externally provided knowledge. Artificial intelligence is not just a game of imagination or a simulated software paradigm but an opposition to increasing economic efficiency. The clear trend of supertechnology will lead human society to cooperate with increasingly intelligent systems, as bright as humans, perhaps even superintelligent. This article presented game theory applications based on artificial intelligence with applicability in ITS management. We proposed a traffic prediction solution based on AI algorithms and game theory.

Research articles that use the k-means technique for generating clusters [24], followed by a principal component analysis to extract the main clustering characteristics to allow the visual representation, may have some limitations due to the choice of the threshold for determining the clusters. Therefore, studies that use modeling conducted by digital travel time curves–map and routing software to traffic prediction [25] may have many advantages. Some studies show that traffic prediction involves learning algorithms such as fuzzy logic, although it faces some problems, such as low accuracy and efficiency [28]. Compared with these works, our research is based on the combination of the golden template algorithm for modeling intersections and making traffic predictions based on game theory and multiagent Nash equilibrium. This model brings more accuracy for improving the travel time, the length of traffic queues, the efficiency of travel flows in an unknown and dynamic environment, and the coordination of the agents’ actions and decision making. Consequently, traffic flows entering the intersections are modeled as independent players who must finally reach an agreement.

Modern transport systems include a comprehensive and ever-evolving suite of technologies and applications: from real-time traffic information and e-ticketing to automatic passenger counting, artificial-intelligence-based traffic forecasting, and advanced modeling and prediction applications based on game theory or evolutionary algorithms [33]. The transformation of a city’s transport network into an intelligent system offers benefits on several levels: increased income, active contribution to the increase in the standard of living in cities and citizens’ perception of the authority’s concern for good governance, a catalyst for a healthy economic life of the municipality, improving the efficiency and operational performance of the transport network, mainly due to cost reduction, increased passenger mobility and comfort, and increased use of the transport system.

5. Conclusions

This research develops an approach based on multiagent game theory and on the golden template algorithm, able to predict intersection congestion reduction and plan multimodal transportation routes for public and passenger transportation. Two game models were developed, one based on the profile of the public transport operator using the separate horizons method and the other based on the number of passengers. The obtained results propose strategies for planning public transport and choosing travel routes. It was found that for road transport, the optimal approach is transport by buses and possibly by express buses. Checking the results regarding public transport data from Bucharest shows the applicability of the developed methodology. The proposed method can be used in planning public passenger transport on alternative routes and ITS management decision making. Game theory and intelligent agents are algorithms used in prediction and decision-making processes, allowing the development of mathematical models for solving real-world problems. Prediction and decision making are of great importance in managerial activity in all fields of activity.

The increased mobility of pedestrians through various means of urban travel during daily activities has motivated the study of its impact on crowd dynamics, the simulation of pedestrian flows, and the planning of public transport routes for ITS systems. Pedestrian crowd dynamics are generally predictable in high-density crowds, where pedestrians can move freely, and self-propelled interactions between pedestrians develop. Although each pedestrian has personal preferences, movement dynamics can be modeled as a social crowd force. The corresponding points can be controlled for each individual and represent various behaviors associated with certain mobility situations, such as danger avoidance, crowding, and pushing. In this software development, we use an agent-based model for pedestrian behavior in traffic situations to predict collective human behavior in a dynamic crowd situation. The proposed simulations represent a practical way to reduce travel time and minimize the waiting time of public vehicles in traffic congestion situations.

Moreover, we introduce a push behavior module, leading to an almost accurate crowd dynamics model. The proposed model will be presented as an extension of game theory. The proposed model is for a person who is part of a crowd and lives in a virtual world. This individual, who will henceforth be called the agent, represents the element embodying the system’s intelligence. Therefore, this approach is based on the collective behavior of individual intelligent agents, from whose interactions a group behavior and self-organizing dynamics of the agents will emerge. The proposed microsimulation model uses a mixture of physical and sociopsychological forces to simulate crowd dynamics. We will aim to introduce auxiliary states for modeling push/push behaviors. Pushing or pushing behavior is when an agent tries to force a path through a crowd. This behavior will require changing the modeling of the planning equation, and planning must overcome the interaction forces to allow an agent to push.

The activity of managers in traffic planning is based on estimating the parameters of the evolutionary game matrix using different implementation methods with intelligent agents. The main result of the research in this article is the application of game theory and intelligent agents to traffic planning. In the previous paragraphs, we showed how real-time data could be correlated with historical data obtained in different periods. To achieve excellent results for modern traffic planning, software developers use quantitative and qualitative models of intelligent agents, along with game and evolution theory.

The increased mobility of pedestrians through various means of urban travel during daily activities has motivated further research by studying its impact on crowd dynamics, simulating pedestrian flows, and planning public transport routes for ITS systems.

Author Contributions

Conceptualization, V.R., C.D. and E.V.; methodology, V.R. and A.I.T.; software, C.D.; validation, V.R., E.V., M.C.S. and F.R.; formal analysis, A.I.T., M.C.S. and L.M.; investigation, E.V., V.R., A.I.T., M.C.S. and C.D.; resources, F.R. and L.M.; data curation, F.R. and C.D.; writing—original draft preparation, C.D., V.R. and A.I.T.; writing—review and editing, L.M., M.C.S. and F.R.; visualization, C.D. and E.V.; supervision, V.R. and E.V.; project administration, V.R.; funding acquisition, V.R., L.M. and E.V. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data were obtained from the Romanian Smart City.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures

Figure 1. The component systems of the ITS architecture.

Figure 2. Chart of ITS systems and AI algorithms services.

Figure 3. Simulation of the method of selecting the bus destination using game theory.

Figure 4. Evolution in time of the coordinates with distributed formation control.

Figure 5. Trajectories of the agents with distributed formation control.

Figure 6. Sequences from the cars (the colored rectangles in the figures) traffic modeling of an intersection based on game theory implemented with intelligent multiagent.

Figure 7. Applying the algorithm developed in this study to an intersection.

Figure 8. Traffic conflict detection at intersections (frame 5).

References

1. Morton, S.M. State of the Art of Research in Management Support System, Sloan School of Management Center, Creative Media Partners LLC. 1983; Available online: https://dspace.mit.edu/bitstream/handle/1721.1/49015/stateofartofrese00scot.pdf;sequence=1 (accessed on 30 January 2023).

2. Sprague, R.H., Jr. A Framework for the Development of Decision Support Systems. MIS Q.; 1980; 4, pp. 1-26. [DOI: https://dx.doi.org/10.2307/248957]

3. Parsons, S.; Wooldridge, M. Game theory and decision theory in multi-agent systems. Auton. Agents Multi-Agent Syst.; 2002; 5, pp. 243-254. [DOI: https://dx.doi.org/10.1023/A:1015575522401]

4. Farhadi, F.; Tavafoghi, H.; Teneketzis, D.; Golestani, S.J. An efficient dynamic allocation mechanism for security in networks of interdependent strategic agents. Dyn. Games Appl.; 2019; 9, pp. 914-941. [DOI: https://dx.doi.org/10.1007/s13235-018-0284-4]

5. Goeree, J.K.; Holt, C.A.; Palfrey, T.R. Quantal response equilibria. Behavioural and Experimental Economics; Palgrave Macmillan: London, UK, 2010; pp. 234-242. [DOI: https://dx.doi.org/10.1057/9780230280786_29]

6. Horák, K.; Bošanský, B. Solving partially observable stochastic games with public observations. Proc. AAAI Conf. Artif. Intell.; 2019; 33, pp. 2029-2036. [DOI: https://dx.doi.org/10.1609/aaai.v33i01.33012029]

7. Hota, A.R.; Sundaram, S. Interdependent security games on networks under behavioral probability weighting. IEEE Trans. Control Netw. Syst.; 2016; 5, pp. 262-273. [DOI: https://dx.doi.org/10.1109/TCNS.2016.2600484]

8. Huang, C.T.; Sakib, M.N.; Njilla, L.; Kamhoua, C. A game theoretic approach for making IoT device connectivity decisions during malware outbreak. Proceedings of the 2019 International Conference on Computing, Networking and Communications (ICNC), IEEE; Honolulu, HI, USA, 18–21 February 2019; pp. 457-462. [DOI: https://dx.doi.org/10.1109/ICCNC.2019.8685493]

9. Huang, Y.; Chen, J.; Huang, L.; Zhu, Q. Dynamic games for secure and resilient control system design. Natl. Sci. Rev.; 2020; 7, pp. 1125-1141. [DOI: https://dx.doi.org/10.1093/nsr/nwz218]

10. Tembine, H. COVID-19: Data-driven mean-field-type game perspective. Games; 2020; 11, 51. [DOI: https://dx.doi.org/10.3390/g11040051]

11. Tembine, H.; Le Boudec, J.Y.; El-Azouzi, R.; Altman, E. Mean field asymptotics of Markov decision evolutionary games and teams. Proceedings of the 2009 International Conference on Game Theory for Networks, IEEE; Istanbul, Turkey, 13–15 May 2009; pp. 140-150. [DOI: https://dx.doi.org/10.1109/GAMENETS.2009.5137395]

12. Tsemogne, O.; Hayel, Y.; Kamhoua, C.; Deugoué, G. Game-Theoretic Modeling of Cyber Deception Against Epidemic Botnets in Internet of Things. IEEE Internet Things J.; 2021; 9, pp. 2678-2687. [DOI: https://dx.doi.org/10.1109/JIOT.2021.3081751]

13. Wang, J.; Wang, W.; Wang, C. Modeling and analysis of conflicting information propagation in a finite time horizon. IEEE/ACM Trans. Netw.; 2020; 28, pp. 972-985. [DOI: https://dx.doi.org/10.1109/TNET.2020.2976972]

14. Watkins, N.J.; Nowzari, C.; Pappas, G.J. Robust economic model predictive control of continuous-time epidemic processes. IEEE Trans. Autom. Control; 2019; 65, pp. 1116-1131. [DOI: https://dx.doi.org/10.1109/TAC.2019.2919136]

15. Zhang, L.; Xu, J. Differential security game in heterogeneous device-to-device offloading network under epidemic risks. IEEE Trans. Netw. Sci. Eng.; 2019; 7, pp. 1852-1861. [DOI: https://dx.doi.org/10.1109/TNSE.2019.2955036]

16. Zhang, T.; Zhu, Q. Informational design of dynamic multi-agent system. arXiv; 2021; [DOI: https://dx.doi.org/10.48550/arXiv.2105.03052] arXiv: 2105.03052

17. Altman, E. A stochastic game approach for competition over popularity in social networks. Dyn. Games Appl.; 2013; 3, pp. 313-323. [DOI: https://dx.doi.org/10.1007/s13235-012-0057-4]

18. Bagagiolo, F.; Bauso, D. Mean-field games and dynamic demand management in power grids. Dyn. Games Appl.; 2014; 4, pp. 155-176. [DOI: https://dx.doi.org/10.1007/s13235-013-0097-4]

19. Chang, S.L.; Piraveenan, M.; Pattison, P.; Prokopenko, M. Game theoretic modelling of infectious disease dynamics and intervention methods: A review. J. Biol. Dyn.; 2020; 14, pp. 57-89. [DOI: https://dx.doi.org/10.1080/17513758.2020.1720322]

20. Chen, J.; Huang, Y.; Zhang, R.; Zhu, Q. Optimal curing strategy for competing epidemics spreading over complex networks. IEEE Trans. Signal Inf. Process. Over Netw.; 2021; 7, pp. 294-308. [DOI: https://dx.doi.org/10.1109/TSIPN.2021.3075338]

21. Eksin, C. Control of stochastic disease network games via influential individuals. Proceedings of the 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE; Nice, France, 11–13 December 2019; pp. 6893-6898. [DOI: https://dx.doi.org/10.1109/CDC40024.2019.9029196]

22. Huang, Y.; Kavitha, V.; Zhu, Q. Continuous-time Markov decision processes with controlled observations. Proceedings of the 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE; Monticello, IL, USA, 24–27 September 2019; pp. 32-39. [DOI: https://dx.doi.org/10.1109/ALLERTON.2019.8919744]

23. Isaacs, R. Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization; Courier Corporation: Massachusetts, USA, 1999; ISBN 9780486406824

24. Zambrano-Martinez, J.L.; TCalafate, C.; Soler, D.; Cano, J.C.; Manzoni, P. Modeling and characterization of traffic flows in urban environments. Sensors; 2018; 18, 2020. [DOI: https://dx.doi.org/10.3390/s18072020]

25. Kerner, B.S.; Rehborn, H.; Aleksic, M.; Haug, A. Traffic prediction systems in vehicles. Proceedings of the 2005 IEEE Intelligent Transportation Systems, IEEE; Vienna, Austria, 16 September 2005; pp. 72-77. [DOI: https://dx.doi.org/10.1109/ITSC.2005.1520056]

26. Min, W.; Wynter, L. Real-time road traffic prediction with spatio-temporal correlations. Transp. Res. C Emerg. Technol; 2011; 19, pp. 606-616. [DOI: https://dx.doi.org/10.1016/j.trc.2010.10.002]

27. Costa, C.; Chatzimilioudis, G.; Zeinalipour-Yazti, D.; Mokbel, M.F. Towards real-time road traffic analytics using telco big data. Proceedings of the International Workshop on Real-Time Business Intelligence and Analytics; Munich Germany, 28 August 2017; pp. 1-5. [DOI: https://dx.doi.org/10.1145/3129292.3129296]

28. Zhang, X.; Onieva, E.; Perallos, A.; Osaba, E.; Lee, V. Hierarchical fuzzy rule-based system optimized with genetic algo-rithms for short term traffic congestion prediction. Transp. Res. C Emerg. Technol.; 2014; 43, pp. 127-142. [DOI: https://dx.doi.org/10.1016/j.trc.2014.02.013]

29. Onieva, E.; Milanés, V.; Villagra, J.; Pérez, J.; Godoy, J. Genetic optimization of a vehicle fuzzy decision system for intersections. Expert Syst. Appl.; 2012; 39, pp. 13148-13157. [DOI: https://dx.doi.org/10.1016/j.eswa.2012.05.087]

30. Hodge, V.J.; Krishnan, R.; Austin, J.; Polak, J.; Jackson, T. Short-term prediction of traffic flow using a binary neural network. Neural Comput. Appl.; 2014; 25, pp. 1639-1655. [DOI: https://dx.doi.org/10.1007/s00521-014-1646-5]

31. Habtie, A.B.; Abraham, A.; Midekso, D. Artificial neural network-based real-time urban road traffic state estimation framework. Computational Intelligence in Wireless Sensor Networks: Recent Advances and Future Challenges; Springer: Berlin/Heidelberg, Germany, 2017; pp. 73-97. [DOI: https://dx.doi.org/10.1007/978-3-319-47715-2_4]

32. Porikli, F.; Li, X. Traffic congestion estimation using HMM models without vehicle tracking. Proceedings of the IEEE Intelligent Vehicles Symposium, IEEE; Parma, Italy, 14–17 June 2004; pp. 188-193. [DOI: https://dx.doi.org/10.1109/IVS.2004.1336379]

33. Hernández, R.; Cárdenas, C.; Muñoz, D. Game theory applied to transportation systems in Smart Cities: Analysis of evolutionary stable strategies in a generic car pooling system. Int. J. Interact. Des. Manuf. (IJIDeM); 2018; 12, pp. 179-185. [DOI: https://dx.doi.org/10.1007/s12008-017-0373-4]

34. Abdoos, M. A cooperative multiagent system for traffic signal control using game theory and reinforcement learning. IEEE Intell. Transp. Syst. Mag.; 2020; 13, pp. 6-16. [DOI: https://dx.doi.org/10.1109/MITS.2020.2990189]

35. Cococcioni, M.; Fiaschi, L.; Lermusiaux, P.F. Game Theory for Unmanned Vehicle Path Planning in the Marine Domain: State of the Art and New Possibilities. J. Mar. Sci. Eng.; 2021; 9, 1175. [DOI: https://dx.doi.org/10.3390/jmse9111175]

36. Sedjelmaci, H.; Hadji, M.; Ansari, N. Cyber security game for intelligent transportation systems. IEEE Netw.; 2019; 33, pp. 216-222. [DOI: https://dx.doi.org/10.1109/MNET.2018.1800279]

37. Zhu, W.; Chen, M.; Wang, D.; Ma, D. Policy-combination oriented optimization for public transportation based on the game theory. Math. Probl. Eng.; 2018; 2018, 7510279. [DOI: https://dx.doi.org/10.1155/2018/7510279]

38. Lagos, A.R.; Kordonis, I.; Papavassilopoulos, G.P. Games of social distancing during an epidemic: Local vs. statistical information. Comput. Methods Programs Biomed. Update; 2022; 2, 100068. [DOI: https://dx.doi.org/10.1016/j.cmpbup.2022.100068]

39. Liu, X.; Lin, K.; Wang, L.; Zhang, H. Stochastic evolutionary game analysis between special committees and ceo: Incentive and supervision. Dyn. Games Appl.; 2021; 11, pp. 538-555. [DOI: https://dx.doi.org/10.1007/s13235-020-00372-x]

40. Chen, R.; Yang, Z. A Cooperative Merging Strategy for Connected and Automated Vehicles Based on Game Theory with Transferable Utility. IEEE Trans. Intell. Transp. Syst.; 2022; 23, pp. 19213-19223. [DOI: https://dx.doi.org/10.1109/TITS.2022.3161535]

41. Dai, Y.; Ma, H. Artificial Intelligence: Need, Evolution, and Applications for Transportation Systems. Intelligent Cyber-Physical Systems for Autonomous Transportation; Springer: Cham, Switzerland, 2022; pp. 71-88. [DOI: https://dx.doi.org/10.1007/978-3-030-92054-8_5]

42. Angelidou, M.; Psaltoglou, A.; Komninos, N.; Kakderi, C.; Tsarchopoulos, P.; Panori, A. Enhancing sustainable urban development through smart city applications. J. Sci. Technol. Policy Manag.; 2017; 9, pp. 146-169. [DOI: https://dx.doi.org/10.1108/JSTPM-05-2017-0016]

43. Andersen, T.J. Information technology, strategic decision making approaches and organizational performance in different industrial settings. J. Strateg. Inf. Syst.; 2001; 10, pp. 101-119. [DOI: https://dx.doi.org/10.1016/S0963-8687(01)00043-9]

44. Arnott, D.; Pervan, G. Eight key issues for the decision support systems discipline. Decis. Support Syst.; 2008; 44, pp. 657-672. [DOI: https://dx.doi.org/10.1016/j.dss.2007.09.003]

45. Brown, I. Strategic information systems planning: Comparing espoused beliefs with practice. Proceedings of the 18th European Conference on Information Systems; Pretoria, South Africa, 2010; pp. 1-12. Available online: https://aisel.aisnet.org/ecis2010/140 (accessed on 30 January 2023).

46. Brown, I.T. Testing and extending theory in strategic information systems planning through literature analysis. Inf. Resour. Manag. J. (IRMJ); 2004; 17, pp. 20-48. [DOI: https://dx.doi.org/10.4018/irmj.2004100102]

47. Ameli, M.; Faradonbeh MS, S.; Lebacque, J.P.; Abouee-Mehrizi, H.; Leclercq, L. Departure Time Choice Models in Urban Transportation Systems Based on Mean Field Games. Transp. Sci.; 2022; 56, pp. 1483-1504. [DOI: https://dx.doi.org/10.1287/trsc.2022.1147]

48. Sandholm, W.H. Population Games and Evolutionary Dynamics; MIT Press: Massachusetts, USA, 2010.

49. Smith, J.M. Evolution and the Theory of Games; Cambridge University Press: Cambridge, England, 1982.

50. Lee, I. Pricing and profit management models for SaaS providers and IaaS providers. J. Theor. Appl. Electron. Commer. Res.; 2021; 16, pp. 859-873. [DOI: https://dx.doi.org/10.3390/jtaer16040049]

51. Bourletidis, K.; Triantafyllopoulos, Y. SMEs survival in time of crisis: Strategies, tactics and commercial success stories. Procedia -Soc. Behav. Sci.; 2014; 148, pp. 639-644. [DOI: https://dx.doi.org/10.1016/j.sbspro.2014.07.092]

52. Alyoubi, B.A. Decision support system and knowledge-based strategic management. Procedia Comput. Sci.; 2015; 65, pp. 278-284. [DOI: https://dx.doi.org/10.1016/j.procs.2015.09.079]

53. Fairbank, J.F.; Labianca, G.J.; Steensma, H.K.; Metters, R. Information processing design choices, strategy, and risk management performance. J. Manag. Inf. Syst.; 2006; 23, pp. 293-319. [DOI: https://dx.doi.org/10.2753/MIS0742-1222230110]