Random-Payoff Two-Person Zero-Sum Games

Abstract

Within the framework of chance-constrained programming, this paper formulates two related stochastic models for players competing in a random-payoff two-person zero-sum game. Under certain assumptions, it shows that a one-to-one correspondence (called stochastic pseudoduality) exists between the two formulations at their optimal values, and, furthermore, exact deterministic equivalents can be obtained for these formulations. The optimal solution for a deterministic equivalent can be found by considering an appropriate class of subproblems.