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Beliefs and rationalizability in games with complementarities

  • Mathevet, Laurent

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)).

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File URL: https://mpra.ub.uni-muenchen.de/36032/1/MPRA_paper_36032.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36032.

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Date of creation: 05 Jan 2012
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Handle: RePEc:pra:mprapa:36032
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  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. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers Archive 11920, Iowa State University, Department of Economics.
  3. 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.
  4. 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 587-97, June.
  5. Larry Epstein, 2005. "An Axiomatic Model of Non-Bayesian Updating," RCER Working Papers 521, University of Rochester - Center for Economic Research (RCER).
  6. Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
  7. Vives, Xavier, 2004. "Complementarities and Games: New Developments," CEPR Discussion Papers 4742, C.E.P.R. Discussion Papers.
  8. Sergei Izmalkov & Muhamet Yildiz, 2010. "Investor Sentiments," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 21-38, February.
  9. Vives, X., 1988. "Nash Equilibrium With Strategic Complementarities," UFAE and IAE Working Papers 107-88, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  10. Flavio Toxvaerd, 2004. "Strategic Merger Waves: A Theory of Musical Chairs," Discussion Paper Series dp359, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  11. 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.
  12. Mathevet, Laurent A., 2010. "Supermodular mechanism design," Theoretical Economics, Econometric Society, vol. 5(3), September.
  13. Mathevet, Laurent, . "A contraction principle for finite global games," Working Papers 1243, California Institute of Technology, Division of the Humanities and Social Sciences.
  14. Stephen Morris & Hyun Song Shin, 2000. "Rethinking Multiple Equilibria in Macroeconomic Modelling," Cowles Foundation Discussion Papers 1260, Cowles Foundation for Research in Economics, Yale University.
  15. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(02), pages 227-253, October.
  16. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
  17. 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.
  18. Terrance Odean, 1999. "Do Investors Trade Too Much?," American Economic Review, American Economic Association, vol. 89(5), pages 1279-1298, December.
  19. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-77, November.
  20. 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, 03.
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