个体与群体之间的一类博弈问题分析

分析个体与群体之间的一类博弈问题，构造一对多博弈模型。其同时具有Stackelberg模型、演化博弈模仿者动态模型的特点：在博弈的第一阶段，有限理性的群体参与者采取模仿者动态行为；在博弈的第二阶段，完全理性的个体参与者根据群体参与者的策略分布，确定自己的反应函数。博弈达到稳定状态后，群体参与者采取演化稳定策略，而个体参与者的风险占优策略将收敛于Nash均衡策略。讨论模型的一些性质：有限理性的群体在模仿过程中存在收益损失；老练的个体参与者存在欺骗行为；在个体参与者完全理性决策的带引下，可以解决多重Nash均衡的选择问题。

An Analysis of a Game Problem Analyze between Individual and Group

This paper analyses the game model between individual and colony that has the characteristics of Stackelberg (model) and replicator dynamic model in evolutionary game. In the game first phase, the bounded rationality colony players (adopt) the replicator dynamic behavior. In the second phase, the full rationality individual player decides the own response (function) by the strategies distribution of colony players. This model has some characteristics as follows. The bounded (rationality) colony players have the payoff losing in the imitating course. The individual player could take the cheat behavior. The colony players can build the form of collusion avoiding the payoff losing. If the game has multiple Nash equilibriums, the foresighted individual player will take the Nash equilibrium strategy that is the Pareto-optimality. In this case the game could reach the multiple Nash equilibriums select.