矩阵对策的公平性研究(英文)

A Study on Equitablity of a Matrix Game

众所周知,零和二人有限对策也称为矩阵对策.设做一个矩阵对策的两个局中人都希望对策结果尽可能公平.当两个局中人使用对策解中的策略进行对策时,如果对策结果最公平,那么这个对策解称为最优的.本文证明了最优对策解集的一些性质,然后给出矩阵对策公平度的概念并证明了它的一些有趣的性质.

It is common knowledge that a zero sum two-person finite game is also called matrix game. Suppose two players who play a matrix game hope that the game result is as equitable as possible. A game solution is called optimal if the game result is most equitable when two players use the strategies in the game solution. In this paper, we prove some properties of a set of optimal game solutions. And we also give the concept of equitable degree of a matrix game and prove some interesting results about it.