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Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets

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  • Alexander Zimper

    (University of Mannheim)

Abstract

For games with expected utility maximizing players whose strategy sets are finite, Pearce (1984) shows that a strategy is strictly dominated by some mixed strategy, if and only if, this strategy is not a best response to some belief about opponents' strategy choice. This note generalizes Pearce''s (1984) equivalence result to games with expected utility maximizing players whose strategy sets are arbitrary compact sets.

Suggested Citation

  • Alexander Zimper, 2005. "Equivalence between best responses and undominated strategies: a generalization from finite to compact strategy sets," Economics Bulletin, AccessEcon, vol. 3(7), pages 1-6.
    • Handle: RePEc:ebl:ecbull:eb-04c70019
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    References listed on IDEAS

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    1. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    2. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    3. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
    4. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    5. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
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    Cited by:

    1. Damianov, Damian S. & Becker, Johannes Gerd, 2010. "Auctions with variable supply: Uniform price versus discriminatory," European Economic Review, Elsevier, vol. 54(4), pages 571-593, May.
    2. Sudhir A. Shah, 2023. "General dualities between best replies and undominated actions," Working papers 337, Centre for Development Economics, Delhi School of Economics.
    3. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economics Research Papers 2014-032, Friedrich-Schiller-University Jena.
    4. Bulat Gafarov & Bruno Salcedo, 2015. "Ordinal dominance and risk aversion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 287-298, October.
    5. Tijmen Daniëls, 2008. "Pure strategy dominance with quasiconcave utility functions," Economics Bulletin, AccessEcon, vol. 3(54), pages 1-8.
    6. Trost, Michael, 2019. "On the equivalence between iterated application of choice rules and common belief of applying these rules," Games and Economic Behavior, Elsevier, vol. 116(C), pages 1-37.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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