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A discrete fractional-order Cournot duopoly game
Physica A: Statistical Mechanics and its Applications ( IF 3.3 ) Pub Date : 2020-07-30 , DOI: 10.1016/j.physa.2020.124993
Baogui Xin , Wei Peng , Yekyung Kwon

This paper focuses on associating the Cournot duopoly problem with long-memory effects. First of all, we generate a discrete fractional-order Cournot duopoly game by introducing the Caputo fractional-order difference calculus to the classical duopoly theory. In the fractional-order game, participants can make their decisions by taking full advantage of their historical information. Then we discuss both Nash equilibria and local stability of the game by employing the linear approximation theory. At last, we numerically validate the main results by using bifurcation diagrams, phase portraits, the largest Lyapunov exponent, and the 0–1 test algorithms.



中文翻译:

离散分数阶古诺双寡头博弈

本文着重将古诺双寡头问题与长记忆效应相关联。首先,通过将Caputo分数阶差微积分引入经典的双寡头理论,我们生成了离散的分数阶Cournot双寡头博弈。在分数阶游戏中,参与者可以充分利用自己的历史信息来做出决策。然后,我们采用线性逼近理论来讨论纳什均衡和博弈的局部稳定性。最后,我们使用分叉图,相图,最大的Lyapunov指数和0-1测试算法对主要结果进行数值验证。

更新日期:2020-07-30
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