Two-Person Zero Sum Games with Random Rewards

Abstract

We consider bi-matrix games between a row player and a column player. The row player’s pay-off depends on a part that is determined by the strategy choices of both players plus a part that depends solely on what is chosen by the column player. Similarly, the column player’s pay-off depends on a part that is determined by the strategy choices of both players plus a part that depends solely on what is chosen by the row player. The sum of the parts of the payoffs that depend on the strategies of both players is equal to zero. We show that a strategy profile is an equilibrium for such a game if and only if it is an equilibrium for the two-person zero-sum game determined by the interdependent parts of the pay-off matrices. Thus, an equilibrium for the kind of game we introduce here exists and the set of equilibria of any such game is equal to the projection of the set of solutions of a corresponding linear programming problem into the set of all strategy profiles.