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Stochastic dominance equilibria in two-person noncooperative games

Author

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  • Andres Perea
  • Hans Peters

    ()

  • Tim Schulteis
  • Dries Vermeulen

Abstract

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 sequenceof t-equilibria.
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Suggested Citation

  • Andres Perea & Hans Peters & Tim Schulteis & Dries Vermeulen, 2006. "Stochastic dominance equilibria in two-person noncooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 457-473, November.
  • Handle: RePEc:spr:jogath:v:34:y:2006:i:4:p:457-473
    DOI: 10.1007/s00182-006-0035-4
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    File URL: http://hdl.handle.net/10.1007/s00182-006-0035-4
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Hans Peters & Tim Schulteis & Dries Vermeulen, 2010. "Generalized stochastic dominance and bad outcome aversion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(2), pages 285-290, July.
    2. Jacques Durieu & Hans Haller & Nicolas Querou & Philippe Solal, 2008. "Ordinal Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 177-194.

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