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Beliefs and rationalizability in games with complementarities

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  • Mathevet, Laurent

Abstract

We propose two characteristics of beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how “favorable” a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles; the second gives a lower bound on the change of location of this set. These bounds are explicit expressions that involve type-sensitivity, optimism, and payoff characteristics. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme, 1993). They also imply new uniqueness results and allow us to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet, 2010b) and information processing errors.

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  • Mathevet, Laurent, 2014. "Beliefs and rationalizability in games with complementarities," Games and Economic Behavior, Elsevier, vol. 85(C), pages 252-271.
    • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:252-271
    DOI: 10.1016/j.geb.2014.02.005
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    Cited by:

    1. Wolfgang Kuhle, 2013. "A Global Game with Heterogenous Priors," Papers 1312.7860, arXiv.org.
    2. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    3. Dominik Grafenhofer & Wolfgang Kuhle, 2019. "Observing Actions in Bayesian Games," Papers 1904.10744, arXiv.org.
    4. Beggs Alan W., 2013. "Dependence and Uniqueness in Bayesian Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 1-25, May.
    5. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    6. Munther A. Dahleh & Alireza Tahbaz-Salehi & John N. Tsitsiklis & Spyros I. Zoumpoulis, 2016. "Technical Note—Coordination with Local Information," Operations Research, INFORMS, vol. 64(3), pages 622-637, June.

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    More about this item

    Keywords

    Complementarities; Rationalizability; Beliefs; Type-sensitivity; Optimism; Global games; Equilibrium uniqueness;
    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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