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Equilibrium payoffs in finite games

Author

Listed:
  • Ehud Lehrer

    (TAU - Tel Aviv University)

  • Eilon Solan

    (TAU - Tel Aviv University)

  • Yannick Viossat

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study the structure of the set of equilibrium payoffs in finite games, both for Nash equilibrium and correlated equilibrium. A nonempty subset of R^2 is shown to be the set of Nash equilibrium payoffs of a bimatrix game if and only if it is a finite union of rectangles. Furthermore, we show that for any nonempty finite union of rectangles U and any polytope P in R^2 containing U, there exists a bimatrix game with U as set of Nash equilibrium payoffs and P as set of correlated equilibrium payoffs. The n-player case and the robustness of this result to perturbation of the payoff matrices are also studied.

Suggested Citation

  • Ehud Lehrer & Eilon Solan & Yannick Viossat, 2011. "Equilibrium payoffs in finite games," Post-Print hal-00361914, HAL.
    • Handle: RePEc:hal:journl:hal-00361914
    DOI: 10.1016/j.jmateco.2010.10.007
    Note: View the original document on HAL open archive server: https://hal.science/hal-00361914
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    References listed on IDEAS

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    1. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
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    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
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    6. David Avis & Gabriel Rosenberg & Rahul Savani & Bernhard Stengel, 2010. "Enumeration of Nash equilibria for two-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 9-37, January.
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    Cited by:

    1. Yehuda John Levy, 2016. "Projections and functions of Nash equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 435-459, March.

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