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Robust equilibria under non-common priors

Author

Listed:
  • Daisuke Oyama

    (Graduate School of Economics - Hitotsubashi University - Hitotsubashi University)

  • Olivier Tercieux

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.

Suggested Citation

  • Daisuke Oyama & Olivier Tercieux, 2010. "Robust equilibria under non-common priors," Post-Print halshs-00754466, HAL.
  • Handle: RePEc:hal:journl:halshs-00754466
    DOI: 10.1016/j.jet.2009.10.009
    Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754466
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    References listed on IDEAS

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    Cited by:

    1. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, vol. 74(1), pages 321-331.
    2. Gensbittel, Fabien & Pęski, Marcin & Renault, Jérôme, 2022. "Value-based distance between information structures," Theoretical Economics, Econometric Society, vol. 17(3), July.
    3. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    4. Atsushi Kajii & Stephen Morris, 2020. "Notes on “refinements and higher order beliefs”," The Japanese Economic Review, Springer, vol. 71(1), pages 35-41, January.
    5. Lu, Shih En, 2017. "Coordination-free equilibria in cheap talk games," Journal of Economic Theory, Elsevier, vol. 168(C), pages 177-208.
    6. 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.
    7. Oyama, Daisuke & Takahashi, Satoru, 2015. "Contagion and uninvadability in local interaction games: The bilingual game and general supermodular games," Journal of Economic Theory, Elsevier, vol. 157(C), pages 100-127.
    8. Ronald Stauber, 2014. "A framework for robustness to ambiguity of higher-order beliefs," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 525-550, August.
    9. Kunimoto, Takashi, 2020. "Robust virtual implementation with almost complete information," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 62-73.

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    More about this item

    Keywords

    Robustness; Incomplete information; Common prior assumption; Higher order belief;
    All these keywords.

    JEL classification:

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

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