矩阵对策上的计策理论

Theory of tricks on a matrix game

设给定的矩阵对策不是平凡的没意义(既不是对局中人1绝对有利,也不是对局中人2绝对有利).在经典矩阵对策系统上加入局中人的判断和佯策略等成分,就得到可以使用计策的矩阵对策系统.文章通过实例给出矩阵对策上的计策的初等概念和严格概念,以Lebesgue测度为工具分别研究了一个局中人中另一个局中人的计的概率和识破另一个局中人的计的概率.最后在欧氏空间上给出一个关于判断的一致连续函数,以此可依次刻画局中人中计,识破计策,以及断定另一个局中人保守的程度.

In this paper, we research theory of tricks on a matrix game. Suppose that the given matrix game is significant, for example, it is absolutely favorable for neither of the two players. We can obtain a matrix game system with tricks if 'judgement' and 'sham strategies' are added to the classical matrix game system. By living examples, we give elementary and strict concepts of tricks on a matrix game. We also research on the probability that a player is trapped into the other one's tricks and the probability that a player sees through the other one's tricks by using Lebesgue measure. Finally, we give a uniform continuous function of judgement on Euclidean space, which can describe some extent to which a player is trapped into a trick, sees through a trick, and believes the other player to be conservative.