具有差异决策规则的产量博弈混沌复杂性研究

Research on chaos complexity of output game with different decision rules

基于有限理性策略与朴素决策规则构建了双寡头产量博弈模型,并提出了用状态延迟和加权平均相结合的方法对竞争对手的预期产量进行估计.通过引入辅助变量并利用Jury判据,分析了该模型的稳定性.结果表明,该博弈模型有一个不稳定的边界不动点和一个局部稳定的纳什平衡点.数值仿真进一步证实,产量调节速度与权重的组合值超出局部稳定性区域时会引起复杂的产量响应,例如,分岔与混沌.获取纳什均衡利润是双方产量博弈的最优结果.

Based on the bounded rational strategy and naive decision-making rule, this paper constructs a game model of duopoly outputs and proposes a combination method with state delay and weighted average to estimate the competitor＇s expected output. Then the model＇s stability is analyzed by introducing auxiliary variable and employing Jury＇s criteria. The results show that the game model has an unstable boundary fixed point and a local stable Nash equilibrium point. Numerical simulations further confirm that when the combination values of the output adjustment speed and the weight are outside the local stability region, the complex output response, such as bifurcation and chaos, will appear. Obtaining Nash equilibrium profits are the optimal result for the output game of both sides.