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Finite Population Dynamics and Mixed Equilibria

Author

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  • Carlos Alós-Ferrer

    (Department of Economics, University of Vienna, Hohenstaufengasse 9, A-1010 Vienna, Austria)

Abstract

This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the2×2case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.

Suggested Citation

  • Carlos Alós-Ferrer, 2003. "Finite Population Dynamics and Mixed Equilibria," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 263-290.
    • Handle: RePEc:wsi:igtrxx:v:05:y:2003:i:03:n:s0219198903001057
    DOI: 10.1142/S0219198903001057
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    References listed on IDEAS

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    1. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
    2. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    3. Carlos Alós-Ferrer, 2000. "Learning, Memory, and Inertia," Vienna Economics Papers 0003, University of Vienna, Department of Economics.
    4. John F. Nash Jr, 1996. "Essays on Game Theory," Books, Edward Elgar Publishing, number 1089.
    5. Oechssler, Jorg, 1997. "An Evolutionary Interpretation of Mixed-Strategy Equilibria," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 203-237, October.
    6. Alos-Ferrer, C., 1998. "Individual Randomness in Economic Models with a Continuum Agents," Papers 9807, Washington St. Louis - School of Business and Political Economy.
    7. Boylan, Richard T., 1992. "Laws of large numbers for dynamical systems with randomly matched individuals," Journal of Economic Theory, Elsevier, vol. 57(2), pages 473-504, August.
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    Citations

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    Cited by:

    1. Carlos Alós-Ferrer & Georg Kirchsteiger & Markus Walzl, 2010. "On the Evolution of Market Institutions: The Platform Design Paradox," Economic Journal, Royal Economic Society, vol. 120(543), pages 215-243, March.
    2. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2006. "Imitation, local interactions, and efficiency," Economics Letters, Elsevier, vol. 93(2), pages 163-168, November.
    3. Carlos Alós-Ferrer & Georg Kirchsteiger, 2015. "Learning and market clearing: theory and experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 203-241, October.
    4. 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.
    5. van Hoesel, C.P.M. & van der Kraaij, A.F. & Mannino, C. & Oriolo, G. & Bouhtou, M., 2003. "Polynomial cases of the tarification problem," Research Memorandum 053, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Thomas Norman, 2010. "Cycles versus equilibrium in evolutionary games," Theory and Decision, Springer, vol. 69(2), pages 167-182, August.
    7. Alos-Ferrer, C. & Kirchsteiger, G., 2003. "Does learning lead to coordination on market clearing institutions," Research Memorandum 038, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    Keywords

    Mixed-strategy Nash equilibrium; imitation dynamics; best reply dynamics; learning; JEL classification code: C72; C73; D83;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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