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Saddle functions and robust sets of equilibria

Author

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  • NORA, Vladyslav

    (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium)

  • UNO, Hiroshi

    (Graduate School of Economics, Osaka Prefecture University, Japan)

Abstract

This paper introduces games with a saddle function. A saddle function is a real valued function on the set of action profiles such that, for one player, minimizing the function implies choosing her best-response, and, for the other players, maximizing it implies choosing their best-responses. We provide a new sufficient condition for robustness to incomplete information of sets of equilibria in a sense of Kajii and Morris (1997, Econometrica), Morris and Ui (2005, J. of Econ. Theory) for games with a saddle function. Our result unifies and generalizes sufficient conditions for zero-sum and best-response potential games.

Suggested Citation

  • NORA, Vladyslav & UNO, Hiroshi, 2012. "Saddle functions and robust sets of equilibria," LIDAM Discussion Papers CORE 2012050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2012050
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    Cited by:

    1. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    2. Kota Murayama, 2020. "Robust predictions under finite depth of reasoning," The Japanese Economic Review, Springer, vol. 71(1), pages 59-84, January.
    3. Kota Murayama, 2015. "Robust Predictions under Finite Depth of Reasoning," Discussion Paper Series DP2015-28, Research Institute for Economics & Business Administration, Kobe University.
    4. Daisuke Oyama & Satoru Takahashi, 2020. "Generalized Belief Operator and Robustness in Binary‐Action Supermodular Games," Econometrica, Econometric Society, vol. 88(2), pages 693-726, March.

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    More about this item

    Keywords

    incomplete information; robust equilibrium; potential games; zero-sum games; team-maximin equilibrium;
    All these keywords.

    JEL classification:

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

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