Dynamics of a Cournot Duopoly Game with a Generalized Bounded Rationality

Abstract

In this paper, the dynamics of Cournot duopoly game with a generalized bounded rationality is considered. The fractional bounded rationality of the Cournot duopoly game is introduced. The conditions of local stability analysis of equilibrium points of the game are derived. The effect of fractional marginal profit on the game is investigated. The complex dynamics behaviors of the game are discussed by numerical computation when parameters are varied.

Game Theory Applications in Micro and Macroscopic Simulations in Transportation Networks: A Comprehensive Review

“…Game of bounded rationality: While GT has had a lot of success, some individuals have questioned whether the participants are rational. Because it is founded on the concept that each player wants the optimal outcome but can only earn restricted payoffs, a bounded rational game is considerably closer to reality [24].…”

A Stochastic Discrete Fractional Cournot Duopoly Game: Modeling, Stability, and Optimal Control

“…Diferential or diference equations are usually used as a powerful analytical tool to study complex behavior in economics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, this kind of model just considers what occurs in the present state but ignores past phases of the process, or what has occurred in earlier states [18].…”

The effect of caputo fractional difference operator on a novel game theory model

“…In [2] chaotic phenomena discovered in a fractionalorder discrete-time Cournot duopoly game are analysed. In [3] the dynamics of Cournot duopoly game with fractional bounded rationality are analyzed. The local stability properties of the equilibrium points are studied, along with the effects of the fractional marginal profit on the game dynamics [3].…”

“…In [3] the dynamics of Cournot duopoly game with fractional bounded rationality are analyzed. The local stability properties of the equilibrium points are studied, along with the effects of the fractional marginal profit on the game dynamics [3]. In [17] a fractional-order discrete Cournot duopoly game model is introduced, which allows participants to make decisions while making full use of their historical information.…”