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Saddle functions and robust sets of equilibria

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  • Nora, Vladyslav
  • Uno, Hiroshi

Abstract

We provide a new sufficient condition for the robustness of sets of equilibria to incomplete information in the sense of Kajii and Morris (1997) [11], Morris and Ui (2005) [15]. The condition is formulated for games with a saddle function. A saddle function is a real-valued function on the set of action profiles such that there is a single player for whom minimizing the function implies choosing her best response, and for the other players maximizing the function implies choosing their best responses. In a game with a saddle function the set of correlated equilibria that induce an expectation of the saddle function greater or equal to its maximin value is robust to incomplete information.

Suggested Citation

  • Nora, Vladyslav & Uno, Hiroshi, 2014. "Saddle functions and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 150(C), pages 866-877.
    • Handle: RePEc:eee:jetheo:v:150:y:2014:i:c:p:866-877
    DOI: 10.1016/j.jet.2013.10.005
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    Cited by:

    1. Kota Murayama, 2020. "Robust predictions under finite depth of reasoning," The Japanese Economic Review, Springer, vol. 71(1), pages 59-84, January.
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    3. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    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; Robustness; Potential; Team-maximin equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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