Stochastic dominance equilibria in two-person noncooperative games
AbstractTwo-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 sequenceof t-equilibria.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 004.
Date of creation: 2005
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Other versions of this item:
- Andres Perea & Hans Peters & Tim Schulteis & Dries Vermeulen, 2006. "Stochastic dominance equilibria in two-person noncooperative games," International Journal of Game Theory, Springer, vol. 34(4), pages 457-473, November.
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- Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
- Borgers, Tilman, 1993. "Pure Strategy Dominance," Econometrica, Econometric Society, vol. 61(2), pages 423-30, March.
- Jacques Durieu & Hans Haller & Nicolas Quérou & Philippe Solal, 2007.
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