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Evolution and Refinement with Endogenous Mistake Probabilities

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  • van Damme, Eric

    (Tilburg University)

  • Weibull, Jörgen W.

    (The Research Institute of Industrial Economics)

Abstract

Bergin and Lipman (1996) show that the refinement effect from the random mutations in the adaptive population dynamics in Kandori, Mailath and rob (1993) and Young (1993) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some effort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). The approach also yields a new refinement of the Nash equilibrium concept that is logically independent of Selten's (1975) perfection concept and Myerson's (1978) properness concept.

Suggested Citation

  • van Damme, Eric & Weibull, Jörgen W., 1999. "Evolution and Refinement with Endogenous Mistake Probabilities," Working Paper Series 525, Research Institute of Industrial Economics.
    • Handle: RePEc:hhs:iuiwop:0525
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    References listed on IDEAS

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    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. 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.
    3. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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    8. Bergin, James & Lipman, Barton L, 1996. "Evolution with State-Dependent Mutations," Econometrica, Econometric Society, vol. 64(4), pages 943-956, July.
    9. van Damme, E.E.C. & Weibull, J., 1998. "Evolution with Mutations Driven by Control Costs," Other publications TiSEM 197ad72d-2cb6-49c3-a875-e, Tilburg University, School of Economics and Management.
    10. Robles, Jack, 1998. "Evolution with Changing Mutation Rates," Journal of Economic Theory, Elsevier, vol. 79(2), pages 207-223, April.
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    Cited by:

    1. van Damme, Eric & Weibull, Jorgen W., 2002. "Evolution in Games with Endogenous Mistake Probabilities," Journal of Economic Theory, Elsevier, vol. 106(2), pages 296-315, October.
    2. Mattsson, Lars-Goran & Weibull, Jorgen W., 2002. "Probabilistic choice and procedurally bounded rationality," Games and Economic Behavior, Elsevier, vol. 41(1), pages 61-78, October.

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    More about this item

    Keywords

    Game theory; Evolutionary game theory; refinement;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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