几个双矩阵经济管理理性博弈的期望均衡分析

An Analysis of Expected Equilibrium in Economical Management Bi-matrix Rational Games

关于完全信息静态博弈,有纯Nash均衡、混合Nash均衡和相关均衡等概念。如果每个参与人除了博弈的结构以外其他一无所知是全体参与人的共同知识(称为完全静态的),那么期望均衡是在极大熵准则是全体参与人的共同知识的条件下的一种均衡。本文首先介绍理性博弈及其期望均衡的概念,然后由此分析了在文献中经常出现的一些经济管理博弈的期望均衡的结果,并与混合Nash均衡结果进行比较。说明对于完全静态博弈,当参与人比通常情况下聪明(极大熵准则是他们的共同知识)的时候,其决策结果比混合Nash均衡更为确定和具有理性。

In a static game with complete information, we have the concepts of pure Nash equilibrium, mixed Nash equilibrium and correlated equilibrium. If it is all the players＇ common knowledge that every player knows nothing except structure of the game, called completely static, then a so called expected equilibrium was defined that is an equilibrium in the case that maximum entropy principle is all the players＇ common. In this paper, we introduce the concepts of a rational game and its expected equilibrium, then analysis the expected equilibrium in some economical management games in many literatures. We compare the expected equilibrium with mixed Nash equilibrium in these games as well. The results show that for a completely static game the players＇ decision results are more certain and rational if they are more intelligent, i.e. maximum entropy principle is their common knowledge.