实质矩阵对策的一个充要条件

设A为对策值是v 的矩阵对策G的赢得矩阵 ,a ,b分别是A的最大元素和最小元素 如果A的第i行元素都是a ,那么只要局中人 1坚持用纯策略i,不论局中人 2用何策略 ,局中人 1都将获最好赢得a ,此类“对策”实质上不是真正的对策 ,故称为 1—非实质对策 类似地 ,若A的第j列元素都是b ,则称G为 2—非实质对策 1—非实质和 2—非实质对策统称为非实质对策 ;否则称实质对策 笔者证明了如下结果 :G为 1—非实质对策的充要条件是v =a .G为 2—非实质对策的充要条件是v =b .G为实质对策的充要条件是b

A Necessary and Sufficient Condition for an Essential Matrix Game

Let A be the payoff matrix of a matrix game G whose game value is v * .Let a and b be the greatest and smallest elements of A,respectively.If the elements in the i th row are all a ,the player 1 obtains always the best payment a provided he uses the pure strategy i .This game is not a true game.So it is called a 1 inessential matrix game.Similarily,the game whose payoff matrix has the property that each element in the j th cloumn is b is called 2 inessential.A matrix game is called inessential if it is either 1 inessential or 2 inessential.An essential maix game is not inessential.In this paper,the author proves the results: G is a 1 inessential game if and only if v *=a ;G is a 2 inessential game if and only if v *=b ;G is an essential if and only if b