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Beliefs and rationalizability in games with complementarities

Author

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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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    1. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    2. Larry G. Epstein, 2006. "An Axiomatic Model of Non-Bayesian Updating," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(2), pages 413-436.
    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.
    4. Toxvaerd, Flavio, 2008. "Strategic merger waves: A theory of musical chairs," Journal of Economic Theory, Elsevier, vol. 140(1), pages 1-26, May.
    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.
    6. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    7. Sergei Izmalkov & Muhamet Yildiz, 2010. "Investor Sentiments," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 21-38, February.
    8. 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.
    9. repec:cup:cbooks:9780521818728 is not listed on IDEAS
    10. 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.
    11. 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.
    12. 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.
    13. repec:cup:cbooks:9780521524131 is not listed on IDEAS
    14. , A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
    15. 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.
    16. repec:cup:cbooks:9780521818742 is not listed on IDEAS
    17. Vives, Xavier, 2004. "Complementarities and Games: New Developments," CEPR Discussion Papers 4742, C.E.P.R. Discussion Papers.
    18. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in Economics and Econometrics: Theory and Applications, Eighth World Congress," ULB Institutional Repository 2013/176003, ULB -- Universite Libre de Bruxelles.
    19. repec:cup:cbooks:9780521524117 is not listed on IDEAS
    20. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    21. Morris, Stephen & Shin, Hyun Song & Yildiz, Muhamet, 2016. "Common belief foundations of global games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 826-848.
    22. Vives, Xavier, 1990. "Nash equilibrium with strategic complementarities," Journal of Mathematical Economics, Elsevier, vol. 19(3), pages 305-321.
    23. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    24. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    25. repec:cup:cbooks:9780521818735 is not listed on IDEAS
    26. repec:cup:cbooks:9780521524124 is not listed on IDEAS
    27. Terrance Odean, 1999. "Do Investors Trade Too Much?," American Economic Review, American Economic Association, vol. 89(5), pages 1279-1298, December.
    28. Mathias Dewatripont & Lars Peter Hansen & Stephen Turnovsky, 2003. "Advances in economics and econometrics :theory and applications," ULB Institutional Repository 2013/9557, ULB -- Universite Libre de Bruxelles.
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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. 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. Manili, Julien, 2024. "Order independence for rationalizability," Games and Economic Behavior, Elsevier, vol. 143(C), pages 152-160.
    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.
    6. Dominik Grafenhofer & Wolfgang Kuhle, 2019. "Observing Actions in Bayesian Games," Papers 1904.10744, arXiv.org.

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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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