广义Nash平衡点和切换控制在对策论中的应用

Generalized Nash Equilibrium and Switched Control in Game Theory

通过把平衡点和决策者的动机耦合的方法,提出了广义纳什平衡点这一新概念。决策者的动机通常有两类: 一是最大化自己的利益,另一则是最大化对手的利益。如果每一个决策者的动机都是第一类,一个理性的群体就会形成, 整个系统最终会达到第一类平衡点(也就是经典的纳什平衡点)。如果每一个决策者的动机都是第二类,一个有智慧的群体就会形成,整个系统最终会达到第二类平衡点。同时,切换控制被用来帮助决策者确定他们的动机。

A new concept of generalized Nash equilibrium is introduced by coupling it with each player＇s incentive. There are two type of incentive： ＂maximize his/her own expected utility payff＂ and ＂maximize the opponent＇s utility payoff＂. If each player is rational and intends to maximize his/her own expected utility payoff, then it will yield a conventional Nash equilibrium （also the frst type of generalized Nash equilibrium）.On the other hand, if each player is wise and intends to maximize the opponent＇s utility payoff, then the second type of generalized Nash equilibrium is obtained. This extension may be an effcient way to apply the concept of Nash equilibrium to the cooperative game. Furthermore, the concept of switched control is used to help each player determine his/her incentive.