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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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    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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