最小最大值定理的几种典型证法

Four Typical Proofs of the Mini-Max Theorem

给出对策论中的最小最大值定理的三种等价形式,并对分别用数学归纳法、凸集分离定理、单纯形理论和Brouwer不动点定理对最小最大值定理所作的证明,进行了综合表述和点评.

We present three equivalent forms of the Mini-Max Theorem in games theory and four typical proofs of the theorem using mathematical induction, convex set separation theorem, simplex theory and Brouwer' s fixed-point theorem respectively. Furthermore we give them uniform expression and commentary.