On the value of some infinite matrix games

It is shown that a zero-sum two-person noncooperative game A defined by a b ounded infinite matrix in which each row converges to the same real number beta and each column to the same real number ct has a value V(A) if and onl y if alpha less than or equal to beta, in which case alpha less than or equ al to V(A) less than or equal to beta. For any game defined by a bounded in finite matrix A = (a(ij)), a necessary condition for V(A) to exist is that inf(j) lim inf(i) a (ij) less than or equal to sup(j) a(ij).