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Correlated equilibrium and concave games

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Abstract

This paper shows that if a game satisfies the sufficient condition for the existence and uniqueness of a pure-strategy Nash equilibrium provided by Rosen (Econometrica 33:520, 1965), then the game has a unique correlated equilibrium, which places probability one on the unique pure-strategy Nash equilibrium. In addition, it shows that a weaker condition suffices for the uniqueness of a correlated equilibrium. The condition generalizes the sufficient condition for the uniqueness of a correlated equilibrium provided by Neyman (Int J Game Theory 26:223, 1997) for a potential game with a strictly concave potential function.

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Authors and Affiliations

  1. Faculty of Economics, Yokohama National University, 79-3 Tokiwadai, Hodogaya-ku, Yokohama, 240-8501, Japan

    Takashi Ui

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  1. Takashi Ui
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Correspondence to Takashi Ui.

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I thank the editor, an associate editor, and an anonymous referee for detailed comments and suggestions, which have substantially improved this paper. Special thanks are due to the referee for pointing out Lemmas 4 and 5. I acknowledge financial support by The Japan Economic Research Foundation and by MEXT, Grant-in-Aid for Scientific Research. All remaining errors are mine.

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Ui, T. Correlated equilibrium and concave games. Int J Game Theory 37, 1–13 (2008). https://doi.org/10.1007/s00182-007-0098-x

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  • DOI: https://doi.org/10.1007/s00182-007-0098-x

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