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Existence Of Correlated Equilibria

In: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics

Author

Listed:
  • Sergiu Hart
  • David Schmeidler

    (Tel Aviv University, Israel)

Abstract

AbstractAn elementary proof, based on linear duality, is provided for the existence of correlated equilibria in finite games. The existence result is then extended to infinite games, including some that possess no Nash equilibria.

Suggested Citation

  • Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14 World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789814390705_0001
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    Citations

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    Cited by:

    1. Hart, Sergiu & Nisan, Noam, 2018. "The query complexity of correlated equilibria," Games and Economic Behavior, Elsevier, vol. 108(C), pages 401-410.
    2. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    3. Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May.
    4. Fabrizio Germano & Gábor Lugosi, 2007. "Existence of Sparsely Supported Correlated Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 575-578, September.
    5. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    6. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    7. repec:the:publsh:3049 is not listed on IDEAS
    8. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    9. Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
    10. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
    11. Bernhard von Stengel & Françoise Forges, 2008. "Extensive-Form Correlated Equilibrium: Definition and Computational Complexity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 1002-1022, November.
    12. repec:kap:theord:v:83:y:2017:i:4:d:10.1007_s11238-017-9609-9 is not listed on IDEAS
    13. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    14. Voorneveld, Mark, 2007. "The possibility of impossible stairways and greener grass," SSE/EFI Working Paper Series in Economics and Finance 673, Stockholm School of Economics.
    15. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
    16. Michael Chwe, 2006. "Statistical Game Theory," Theory workshop papers 815595000000000004, UCLA Department of Economics.
    17. Jann, Ole & Schottmüller, Christoph, 2015. "Correlated equilibria in homogeneous good Bertrand competition," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 31-37.
    18. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    19. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    20. repec:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-012-9988-6 is not listed on IDEAS
    21. Yang, Zhou, 2006. "Correlated Equilibrium and the Estimation of Static Discrete Games with Complete Information," MPRA Paper 79395, University Library of Munich, Germany.
    22. Noah Stein & Asuman Ozdaglar & Pablo Parrilo, 2011. "Structure of extreme correlated equilibria: a zero-sum example and its implications," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 749-767, November.
    23. Fook Kong & Berç Rustem, 2013. "Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity," Journal of Global Optimization, Springer, vol. 57(1), pages 251-277, September.
    24. Larry Samuelson, 2003. "Imperfect Monitoring and Impermanent Reputations," Theory workshop papers 505798000000000030, UCLA Department of Economics.
    25. Rabah Amir & Sergei Belkov & Igor V. Evstigneev, 2017. "Correlated equilibrium in a nutshell," Theory and Decision, Springer, vol. 83(4), pages 457-468, December.

    More about this item

    Keywords

    Game Theory; Dynamics; Equilibrium; Nash Equilibrium; Correlated Equilibrium; Adaptive Dynamics; Simple Strategies; Regret-Based Strategies; Uncoupled Dynamics; Bounded Rationality;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

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