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The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games

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  • Viossat, Yannick

    (Dept. of Economics, Stockholm School of Economics)

Abstract

A pure strategy is coherent if it is played with positive probability in at least one correlated equilibrium. A game is pre-tight if in every correlated equilibrium, all incentives constraints for non deviating to a coherent strategy are tight. We show that there exists a Nash equilibrium in the relative interior of the correlated equilibrium polytope if and only if the game is pre-tight. Furthermore, the class of pre-tight games is shown to include and generalize the class of two-player zero-sum games.

Suggested Citation

  • Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," SSE/EFI Working Paper Series in Economics and Finance 641, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0641
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    Cited by:

    1. 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.
    2. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    3. Stefanos Leonardos & Costis Melolidakis, 2018. "On the Commitment Value and Commitment Optimal Strategies in Bimatrix Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-28, September.
    4. Soham R. Phade & Venkat Anantharam, 2019. "On the Geometry of Nash and Correlated Equilibria with Cumulative Prospect Theoretic Preferences," Decision Analysis, INFORMS, vol. 16(2), pages 142-156, June.
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    More about this item

    Keywords

    correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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