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Received Feb 11, 2017; Revised Mar 22, 2017; Accepted Mar 26, 2017
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1. Introduction
A Triopoly is a market structure dominated by three firms in the market. The market is known as Cournot game if firms choose quantities as their strategic variables to maximize their profits in an uncertain demand environment.
In conventional market games, players are supposed to have common accurate demand functions of market. The dynamics of such system with this assumption have been intensively investigated in literature [1–8].
Assuming cost function to be twice differentiable increasing, Elabbasy et al. [1] analyzed the dynamics of oligopoly games with three types of players: bounded rational, naive, and adaptive.
Ma and Liu [2] studied a generalized nonlinear Fokker-Planck diffusion equation with external force and absorption. They obtained the corresponding exact solution expressed by
Yassen and Agiza [3] studied a repeated Cournot game model with delayed bounded rationality in the duopoly market and demonstrated that the lagged structure is helpful to expand the stable region of the system via numerical simulations.
Ma and Ren [4] focused on the influence of parameters on the macroeconomics IS-LM model and improved the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. They found that the system order has an important influence on the running state of the system.
Tramontana and Elsadany [5] discussed a triopolistic market with heterogeneous firms when the demand function is isoelastic. He found that double routes lead to chaos, via period-doubling and Neimark–Sacker bifurcations.
Ma and Ji [6] built a Triopoly outputs game model in electric power market. They obtained that the Triopoly model is a chaotic system and it is better than the duopoly model in applications.
Ma and Wu [7] studied the complexity of a Triopoly price game model and influence of delayed decisions on the stability. All those approaches assume that there is one uniform and accurate market demand function available and shared by all player.
Ma and Pu [8] researched the...