n人非合作博弈弱Nash均衡点的存在性
The Existence of Weak Nash Equilibrium in n-Person Non-Cooperative Game

DOI：

 作者 单位 蔡阳洋, 向淑文 贵州大学 数学与统计学院,贵阳 550025

根据Nash均衡的定义，也即是局中人单独改变自己的策略不能使自己支付更大这一结论，提出了一种新的均衡，其思想是局中人通过改变自己的策略的确可以增加自己的支付，但是由于局中人改变策略会产生成本这一事实，当成本高于或等于增加的支付时使得局中人没有改变自己的策略。基于这样的事实背景，在博弈模型中引入了局中人的成本函数，重新建立了n人非合作博弈模型，以及n人非合作广义博弈模型，并给出了弱Nash均衡点的定义，在此基础上研究博弈模型中弱Nash均衡点的存在性;通过定义最优回应映射，应用相关引理证明最优回应映射是usco的、非空的、凸的;通过Fan-Glicksberg不动点定理证明了n人非合作博弈，以及n人非合作广义博弈弱Nash均衡点的存在性。

According to the definition of Nash equilibrium, the player can not change his own strategy alone to make his own payment larger，this paper puts forward a new kind of equilibrium, which is that the player can really increase his own payment by changing his own strategy.Because of the fact that the player’s change of strategy will produce cost,however，when the cost is higher than or equal to the increased payment, the player does not change his strategy. Based on this factual background, the cost function of players is introduced into the game model, the n-person non-cooperative game model and n-person non-cooperative generalized game model are reestablished, and the definition of weak Nash equilibrium point is given. On this basis, the existence of weak Nash equilibrium in the game model is studied. By defining the optimal response mapping, it is proved that the optimal response mapping is usco, non-empty and convex by using the correlation lemma. The existence of weak Nash equilibrium point of n-person non-cooperative game and n-person non-cooperative generalized game is proved by Fan-Glicksberg fixed point theorem.