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Beliefs and rationalizability in games with complementarities

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  • Mathevet, Laurent

Abstract

We propose two characteristics of players' 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 have explicit and relatively simple expressions that feature type-sensitivity, optimism, and properties of the payoffs. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme (1993)). They imply new uniqueness results and allow to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet (2010)) and non-Bayesian updating (Epstein (2006)).

Suggested Citation

  • Mathevet, Laurent, 2012. "Beliefs and rationalizability in games with complementarities," MPRA Paper 36032, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36032
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    Cited by:

    1. Wolfgang Kuhle, 2013. "A Global Game with Heterogenous Priors," Papers 1312.7860, arXiv.org.
    2. Dominik Grafenhofer & Wolfgang Kuhle, 2019. "Observing Actions in Bayesian Games," Papers 1904.10744, arXiv.org.
    3. 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.
    4. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    5. 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:

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

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