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Evolution and correlated equilibrium

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  • Lars P. Metzger

    (TU Dortmund University)

Abstract

Given a normal form game and a signal generating process, we construct an expanded game in the spirit of Aumann (Econometrica 55(1):1–18, 1987) in which agents condition their strategic choices on perceived signals. We collect results on evolutionary selection dynamics of Ritzberger and Weibull (Econometrica 63(6):1371–1399, 1995), Swinkels (J Econ Theory 57(2):306–332, 1992b) and Samuelson and Zhang (J Econ Theory 57:363–391, 1992) to apply them to normal form games with payoff irrelevant signals. We suggest a selection dynamic for the evolution of signals and characterize the set of signal distributions and induced payoffs for sets that are asymptotically stable with respect to this evolutionary selection on signals.

Suggested Citation

  • Lars P. Metzger, 2018. "Evolution and correlated equilibrium," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 333-346, April.
    • Handle: RePEc:spr:joevec:v:28:y:2018:i:2:d:10.1007_s00191-017-0539-z
    DOI: 10.1007/s00191-017-0539-z
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    References listed on IDEAS

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    1. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    2. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    4. Sergiu Hart & Andreu Mas-Colell, 2013. "A Simple Adaptive Procedure Leading To Correlated Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 2, pages 17-46, World Scientific Publishing Co. Pte. Ltd..
    5. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    6. Avner Shaked & Larry Samuelson & George J. Mailath, 1997. "Correlated equilibria and local interactions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 551-556.
    7. Koch, Lars P., 2008. "Evolution and Correlated Equilibrium," Bonn Econ Discussion Papers 14/2008, University of Bonn, Bonn Graduate School of Economics (BGSE).
    8. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    9. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
    10. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May.
    11. Lenzo, Justin & Sarver, Todd, 2006. "Correlated equilibrium in evolutionary models with subpopulations," Games and Economic Behavior, Elsevier, vol. 56(2), pages 271-284, August.
    12. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    13. Swinkels, Jeroen M., 1992. "Evolution and strategic stability: From maynard smith to kohlberg and mertens," Journal of Economic Theory, Elsevier, vol. 57(2), pages 333-342, August.
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    Cited by:

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    3. William C. Grant, 2023. "Correlated Equilibrium and Evolutionary Stability in 3-Player Rock-Paper-Scissors," Games, MDPI, vol. 14(3), pages 1-16, May.
    4. Correia, A.D. & Leestmaker, L.L. & Stoof, H.T.C. & Broere, J.J., 2022. "Asymmetric games on networks: Towards an Ising-model representation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).

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    More about this item

    Keywords

    Correlated equilibrium; Replicator dynamics; Evolutionary stability; Asymptotic stability; Evolution of signals;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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