Stochastic dominance equilibria in two-person noncooperative games

Two-person noncooperative games with finitely many pure strategies and ordinal preferences over pure outcomes are considered, in which probability distributions resulting from mixed strategies are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and existence proofs of t-equilibria in terms of representing utility functions, and shows that for t becoming large—which can be interpreted as the players becoming more risk averse—behavior converges to a specific form of max-min play. More precisely, this means that in the limit each player puts all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequence of t-equilibria.