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This paper deals with two-person zero-sum rectangular games with random payoffs. It is assumed that each player knows the distribution functions of the random entries and that players must select their strategies before any observations of the random entries are made. In such a case, several models are considered and relations -among the optimal values are obtained. A special case, in which these random entries are linear functions of a random variable is also treated and some properties of the optimal strategies are given. In the final section, illustrative examples are shown. 1. Preliminaries In many of the practical situations which can be modeled as two-person zero-sum rectangular games, the elements of the payoff matrix may be known to the players as random variables with specified probability distributions. In this paper, we consider a two-person random payoff matrix A = (a . . ). The . 1,J zero-sum rectangular game with an m by n random variable a .. represents the payoff 1,J from player 11 to' player I when player I plays row i and player 11 plays column j. We assume that each player knows the distribution of every random element in A and that the a .. are independent of the mixed strategies selected 't-J by the players. We further assume that the players must select their strate- gies before any observations are taken on the a... Thus, strategies are to be 't-J deterministic and are not to be explicit functions of the a .. , although 't-J

TWO-PERSON ZERO-SUM GAMES WITH RANDOM PAYOFFS