Solution of a Satisficing Model for Random Payoff Games

In this paper, we consider a “satisficing” criterion to solve two-person zero-sum games with random payoffs. In particular, a player wants to maximize the payoff level he can achieve with a specified confidence. The problem reduces to solving a nonconvex mathematical programming problem. The main result shows that solving this problem is equivalent to finding the root of an equation whose values are determined by solving a linear problem. This linear problem results from maximizing the confidence with fixed payoff level.