矩阵计策的支撑解系(英文)

THE SUPPORTING SOLUTION SYSTEMS FOR MATRIX TRICKS

令 [aij]n× n是二人零和对策的支付矩阵 .局中人 1可用其“计策”得到最大支付 a=max{ aij|1≤ i≤ n,1≤ j≤ n} ,然而 ,一个开放问题是如何找到全体计策解 ,本文首先引进计策解系的一种特殊类型支撑解系 .然后研究支撑解系的特征、性质、代数结构 .最后给出寻找全体基本支撑解系的一个算法 .

Let nxn be the payoff matrix of a two person zero sum game.The player 1 can obtain the greatest payment a=max｛a ij ｜I≤i≤m,1≤j≤n｝ by using his “trick”.But,it is an open problem to find all trick solutions.In this paper,we,first,introduce the concept of supporting solution system that is a special form of trick solution system.Then we research the character,properties,and algebraic structure of supporting solution systems.Finally,we give an algorithm for finding all basic supporting solution systems.