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Openness of the set of games with a unique correlated equilibrium

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  • Yannick Viossat

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

Abstract

We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite normal form games with a unique correlated equilibrium is open, while this is not true of Nash equilibrium for n>2. The crucial lemma is that a unique correlated equilibrium is a quasi-strict Nash equilibrium. Related results are studied. For instance, we show that generic two-person zero-sum games have a unique correlated equilibrium and that, while the set of symmetric bimatrix games with a unique symmetric Nash equilibrium is not open, the set of symmetric bimatrix games with a unique and quasi-strict symmetric Nash equilibrium is.

Suggested Citation

  • Yannick Viossat, 2005. "Openness of the set of games with a unique correlated equilibrium," Working Papers hal-00243016, HAL.
    • Handle: RePEc:hal:wpaper:hal-00243016
    Note: View the original document on HAL open archive server: https://hal.science/hal-00243016
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    References listed on IDEAS

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    1. Raghavan, T.E.S., 2002. "Non-zero-sum 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 44, pages 1687-1721, Elsevier.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. 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..
    4. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
    5. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515-515, March.
    6. Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    Cited by:

    1. Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.

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