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An Evolutionary Interpretation of Mixed-Strategy Equilibria

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  • Oechssler, Jorg

Abstract

One of the more convincing interpretations of mixed strategy equilibria describes a mixed equilibrium as a steady state in a large population in which all players use pure strategies but the population as a whole mimics a mixed strategy. To be complete, however, this interpretation requires a good story about how the population arrives at the appropriate distribution over pure strategies. In this paper I attempt to give an explanation based on an evolutionary, stochastic learning process. Convergence properties of these processes have been studied extensively but almost exclusively for the case of convergence to pure Nash equilibria. Here I study the conditions under which an evolutionary process converges to population mixed-strategy equilibria. I find that not all mixed equilibria can be justified as the result of the evolutionary learning process even if the equilibrium is unique. For symmetric 2x2 and 3x3 games I give necessary and sufficient conditions for convergence and for n*n games I give a sufficient condition. For cases in which the conditions are not satisfied counterexamples are given, in which the process enters a limit cycle.
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  • Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
  • Handle: RePEc:eee:gamebe:v:21:y:1997:i:1-2:p:203-237
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    Cited by:

    1. Marie-Laure Cabon-Dhersin & Nathalie Etchart-Vincent, 2013. "Wording and gender effects in a Game of Chicken. An explorative experimental study," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00796708, HAL.
    2. repec:hal:wpaper:hal-00741973 is not listed on IDEAS
    3. DeMichelis, Stefano & Germano, Fabrizio, 2000. "On the Indices of Zeros of Nash Fields," Journal of Economic Theory, Elsevier, vol. 94(2), pages 192-217, October.
    4. Oechssler, Jorg, 1997. "Decentralization and the coordination problem," Journal of Economic Behavior & Organization, Elsevier, vol. 32(1), pages 119-135, January.
    5. Fei Shi, 2015. "Long-run technology choice with endogenous local capacity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 377-399, June.
    6. Jörg Oechssler & Karl H Schlag, 1997. "Loss of Commitment? An Evolutionary Analysis of Bagwell’s Example," Levine's Working Paper Archive 598, David K. Levine.
    7. DE MICHELIS, Stefano & GERMANO, Fabrizio, 2000. "On knots and dynamics in games," CORE Discussion Papers 2000010, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Jorg Oechssler & Karl Schlag, 1997. "An Evolutionary Analysis of Bagwell's Example," Game Theory and Information 9704001, EconWPA, revised 11 Apr 1997.
    9. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October.
    10. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    11. Thomas Norman, 2010. "Cycles versus equilibrium in evolutionary games," Theory and Decision, Springer, vol. 69(2), pages 167-182, August.
    12. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
    13. Wilfred Amaldoss & Robert J. Meyer & Jagmohan S. Raju & Amnon Rapoport, 2000. "Collaborating to Compete," Marketing Science, INFORMS, vol. 19(2), pages 105-126, November.

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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