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Geometry, Correlated Equilibria and Zero-Sum Games

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  • Yannick Viossat

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper is concerned both with the comparative geometry of Nash and correlated equilibria, and with a generalization of zero-sum games based on correlated equilibria. The set of correlated equilibrium distributions of any finite game in strategic form is a polytope, which contains the Nash equilibria. I characterize the class of games such that this polytope (if not a singleton) contains a Nash equilibrium in its relative interior. This class of games, though not defined by some antagonistic property, is shown to include and generalize two-player zero-sum games.

Suggested Citation

  • Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242993
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242993
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    References listed on IDEAS

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    1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    8. Robert W. Rosenthal, 1973. "Correlated Equilibria in Some Classes of Two-Person Games," Discussion Papers 45, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. repec:dau:papers:123456789/3048 is not listed on IDEAS
    10. Cripps, Martin, 1991. "Correlated equilibria and evolutionary stability," Journal of Economic Theory, Elsevier, vol. 55(2), pages 428-434, December.
    11. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
    12. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
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    14. 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..
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    Cited by:

    1. Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    2. repec:dau:papers:123456789/3048 is not listed on IDEAS
    3. Michael Chwe, 2006. "Statistical Game Theory," Theory workshop papers 815595000000000004, UCLA Department of Economics.

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