IDEAS home Printed from https://ideas.repec.org/p/ecm/feam04/495.html
   My bibliography  Save this paper

Evolutionarily Stable Correlation

Author

Listed:
  • Kam-Chau Wong
  • Chongmin Kim

Abstract

Most existing results of evolutionary games restrict only to the Nash equilibrium. This paper introduces the analogue of evolutionarily stable strategy (ESS) for correlated equilibria. We introduce a new notion of evolutionarily stable correlation (ESC) and prove that it generalizes ESS. We also study analogues of perfection (cf. Dhillon and Mertens (1994)), properness, and replicator dynamics for the correlation equilibrium and discuss their relationships with ESC

Suggested Citation

  • Kam-Chau Wong & Chongmin Kim, 2004. "Evolutionarily Stable Correlation," Econometric Society 2004 Far Eastern Meetings 495, Econometric Society.
    • Handle: RePEc:ecm:feam04:495
    as

    Download full text from publisher

    File URL: http://repec.org/esFEAM04/up.16804.1077678412.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. Forges, Francoise & Peck, James, 1995. "Correlated Equilibrium and Sunspot Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 33-50, January.
    3. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
    4. Ianni, Antonella, 2001. "Learning correlated equilibria in population games," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 271-294, November.
    5. 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.
    6. Myerson, Roger B., 1994. "Communication, correlated equilibria and incentive compatibility," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 24, pages 827-847, Elsevier.
    7. Fudenberg, Drew & Levine, David K., 1999. "Conditional Universal Consistency," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 104-130, October.
    8. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    9. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    10. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    12. 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..
    13. Swinkels, Jeroen M., 1992. "Evolutionary stability with equilibrium entrants," Journal of Economic Theory, Elsevier, vol. 57(2), pages 306-332, August.
    14. Foster, Dean P. & Vohra, Rakesh V., 1997. "Calibrated Learning and Correlated Equilibrium," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 40-55, October.
    15. Roger B. Myerson, 1977. "Refinements of the Nash Equilibrium Concept," Discussion Papers 295, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    16. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhigang Cao, 2013. "Bargaining and cooperation in strategic form games with suspended realizations of threats," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 337-358, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kets, Willemien & Kager, Wouter & Sandroni, Alvaro, 2022. "The value of a coordination game," Journal of Economic Theory, Elsevier, vol. 201(C).
    2. Lars P. Metzger, 2018. "Evolution and correlated equilibrium," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 333-346, April.
    3. Friedman, Daniel & Rabanal, Jean Paul & Rud, Olga A. & Zhao, Shuchen, 2022. "On the empirical relevance of correlated equilibrium," Journal of Economic Theory, Elsevier, vol. 205(C).
    4. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    5. Ehud Lehrer & Eilon Solan, 2007. "Learning to play partially-specified equilibrium," Levine's Working Paper Archive 122247000000001436, David K. Levine.
    6. Lenzo, Justin & Sarver, Todd, 2006. "Correlated equilibrium in evolutionary models with subpopulations," Games and Economic Behavior, Elsevier, vol. 56(2), pages 271-284, August.
    7. Michael Foley & Rory Smead & Patrick Forber & Christoph Riedl, 2021. "Avoiding the bullies: The resilience of cooperation among unequals," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-18, April.
    8. Arifovic, Jasmina & Boitnott, Joshua F. & Duffy, John, 2019. "Learning correlated equilibria: An evolutionary approach," Journal of Economic Behavior & Organization, Elsevier, vol. 157(C), pages 171-190.
    9. Stoltz, Gilles & Lugosi, Gabor, 2007. "Learning correlated equilibria in games with compact sets of strategies," Games and Economic Behavior, Elsevier, vol. 59(1), pages 187-208, April.
    10. Chongmin Kim & Kam-Chau Wong, 2017. "Evolutionarily Stable Correlation," Korean Economic Review, Korean Economic Association, vol. 33, pages 55-94.
    11. Ozdogan, Ayca & Saglam, Ismail, 2021. "Correlated equilibrium under costly disobedience," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 98-104.
    12. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    13. Rene Saran & Roberto Serrano, 2012. "Regret Matching with Finite Memory," Dynamic Games and Applications, Springer, vol. 2(1), pages 160-175, March.
    14. Rabah Amir & Sergei Belkov & Igor V. Evstigneev, 2017. "Correlated equilibrium in a nutshell," Theory and Decision, Springer, vol. 83(4), pages 457-468, December.
    15. Luo, Xiao & Qiao, Yongchuan & Sun, Yang, 2022. "A revelation principle for correlated equilibrium under trembling-hand perfection," Journal of Economic Theory, Elsevier, vol. 200(C).
    16. Drew Fudenberg & David K. Levine, 2006. "Superstition and Rational Learning," American Economic Review, American Economic Association, vol. 96(3), pages 630-651, June.
    17. Azrieli, Yaron, 2010. "Categorization and correlation in a random-matching game," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 303-310, May.
    18. Soham R. Phade & Venkat Anantharam, 2023. "Learning in Games with Cumulative Prospect Theoretic Preferences," Dynamic Games and Applications, Springer, vol. 13(1), pages 265-306, March.
    19. Claudia Cerrone & Francesco Feri & Philip R. Neary, 2019. "Ignorance is bliss: a game of regret," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2019_10, Max Planck Institute for Research on Collective Goods.
    20. Yuval Heller & Eyal Winter, 2016. "Rule Rationality," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(3), pages 997-1026, August.

    More about this item

    Keywords

    Correlated Equilibrium; Evolutionarily Stable Correlation; Evolutionarily Stable State; Random Device;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:feam04:495. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.