Stochastic dominance equilibria in two-person non-cooperative games

A. Perea ý Monsuwé, H.J.M. Peters, T.J.W. Schulteis, A.J. Vermeulen

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

Two-person noncooperative games with finitely many pure strategies are considered, in which the players have linear orderings over sure outcomes but incomplete preferences over probability distributions resulting from mixed strategies. These probability distributions 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 an existence proof of t-equilibria in terms of representing utility functions, and shows that for large t behavior converges to a form of max–min play. Specifically, increased aversion to bad outcomes makes each player put 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.
Original languageEnglish
Pages (from-to)457-473
Number of pages17
JournalInternational Journal of Game Theory
Volume34
DOIs
Publication statusPublished - 1 Jan 2006

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