计策理论中的模型(之一)

A Mathematical Model on Stratagem Theory

对策论只给出了收入期望的最小值和相应的最佳策略。怎样才能得到最大收入?这个问题超出了对策论的研究范围。想要得到最大收入,必须使用计策。本文建立了计策理沦的一个模型,并讨论了模型的概念、性质、判定及求法等。初步建立起计策理论的数学体系。

Let A = [aij]mxn be a payoff matrix of two-person zero-sume games and (X* ,Y*) be its equilibrium solution. The player 1, as is known to all ,can obtain the income with the least expected value v* =X* AY*T so long as he persists using his optimum strategy X*. How docs he obtain the greastest value a=max {aij | 1≤i≤ m, 1≤j≤n}? This problem oversteps the scope of game theory.In this paper, we put forward a new theory, which is called Stratagem Theory , to study how player 1 use stratagem to obtain the greatest income a .