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Equivalence between best responses and undominated

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  • Zimper, Alexander

    (Sonderforschungsbereich 504)

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

  • Zimper, Alexander, 2005. "Equivalence between best responses and undominated," Sonderforschungsbereich 504 Publications 05-08, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  • Handle: RePEc:xrs:sfbmaa:05-08
    Note: Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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    File URL: http://www.sfb504.uni-mannheim.de/publications/dp05-08.pdf
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    References listed on IDEAS

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    1. Ghirardato, Paolo & Le Breton, Michel, 2000. "Choquet Rationality," Journal of Economic Theory, Elsevier, vol. 90(2), pages 277-285, February.
    2. R. Guesnerie, 2002. "Anchoring Economic Predictions in Common Knowledge," Econometrica, Econometric Society, vol. 70(2), pages 439-480, March.
    3. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    4. Moulin, Herve, 1984. "Dominance solvability and cournot stability," Mathematical Social Sciences, Elsevier, vol. 7(1), pages 83-102, February.
    5. Werlang, Sérgio Ribeiro da Costa, 1988. "Common knowledge," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 118, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    6. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
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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. Michael Trost, 2014. "On the Equivalence between Iterated Application of Choice Rules and Common Belief of Applying these Rules," Jena Economic Research Papers 2014-032, Friedrich-Schiller-University Jena.
    3. 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.
    4. Tijmen Daniëls, 2008. "Pure strategy dominance with quasiconcave utility functions," Economics Bulletin, AccessEcon, vol. 3(54), pages 1-8.
    5. 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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