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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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    References listed on IDEAS

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    3. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
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    5. Brandenburger, Adam & Dekel, Eddie & Geanakoplos, John, 1992. "Correlated equilibrium with generalized information structures," Games and Economic Behavior, Elsevier, vol. 4(2), pages 182-201, April.
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    7. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 539-563, March.
    8. 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.
    9. Van Zandt, Timothy & Vives, Xavier, 2007. "Monotone equilibria in Bayesian games of strategic complementarities," Journal of Economic Theory, Elsevier, vol. 134(1), pages 339-360, May.
    10. Jonathan Weinstein & Muhamet Yildiz, 2007. "A Structure Theorem for Rationalizability with Application to Robust Predictions of Refinements," Econometrica, Econometric Society, vol. 75(2), pages 365-400, March.
    11. Mathevet, Laurent A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
    12. Stephen Morris & Hyun Song Shin, 2001. "Rethinking Multiple Equilibria in Macroeconomic Modeling," NBER Chapters,in: NBER Macroeconomics Annual 2000, Volume 15, pages 139-182 National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Wolfgang Kuhle, 2013. "A Global Game with Heterogenous Priors," Papers 1312.7860, arXiv.org.
    2. Mathevet, Laurent & Taneva, Ina, 2013. "Finite supermodular design with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 82(C), pages 327-349.
    3. Wolfgang Kuhle, 2016. "A global game with heterogenous priors," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 167-185, October.
    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.

    More about this item

    Keywords

    Complementarities; rationalizability; beliefs; type-sensitivity; optimism; global games; equilibrium uniqueness;

    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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