矩阵博弈的胜利度和“僵局”

Victory Degree and Stalemate in a Matrix Game

矩阵博弈又称有限对抗博弈 ,而对抗博弈的结果必是一方胜利、失败或双方和局。本文首先给出胜利、失败和和局的数学模型 ,接着给出描述胜利程度的概念——胜利度并讨论了胜利度的几个简单性质。依此分析了传统矩阵博弈出现“僵局”的原因并指出排除“僵局”的方法。

A matrix game is also called finite antagonistic game. A result of antagonism is a fixed player's won, lost or drawn game. This paper gives the mathematical model of these concepts, defines victory degree and gives some properties of victory degree. With this we also analyse the reason for a matrix game yields stalemate, and obtain the method to get rid of stalemate.