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Rationalization and Incomplete Information

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Author Info
Pierpaolo Battigalli (Università Bocconi, IEP)
Marciano Siniscalchi (Northwestern University and Princeton University)

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Abstract

We analyze a family of extensive-form solution procedures for games with incomplete information that do not require the specification of an epistemic type space a la Harsanyi, but can accommodate a (commonly known) collection of explicit restrictions D on first-order beliefs. For any fixed D we obtain a solution called D-rationalizability. In static games, D-rationalizability characterizes the set of outcomes (combinations of payoff types and strategies) that may occur in any Bayesian equilibrium model consistent with D; these are precisely the outcomes consistent with common certainty of rationality and of the restrictions D. Hence, our approach to the analysis of incomplete-information games is consistent with Harsanyi's, and it may be viewed as capturing the robust implications of Bayesian equilibrium analysis. In dynamic games, D-rationalizability yields a forward-induction refinement of this set of Bayesian equilibrium outcomes. Focusing on the restriction that first-order beliefs be consistent with a given distribution on terminal nodes, we obtain a refinement of self-confirming equilibrium. In signalling games, this refinement coincides with the Iterated Intuitive Criterion.

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Publisher Info
Article provided by Berkeley Electronic Press in its journal Advances in Theoretical Economics.

Volume (Year): 3 (2003)
Issue (Month): 1 ()
Pages: 1073-1073
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Handle: RePEc:bep:theadv:v:3:y:2003:i:1:p:1073-1073

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Related research
Keywords: Incomplete Information Rationalizability Bayesian Equilibrium Self-Confirming Equilibrium Iterated Intuitive Criterion

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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  2. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  9. Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April. [Downloadable!] (restricted)
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  13. Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September. [Downloadable!] (restricted)
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  14. Pierpaolo Battigalli & Joel Watson, 1997. "On "Reputation" Refinements with Heterogeneous Beliefs," Econometrica, Econometric Society, vol. 65(2), pages 369-374, March.
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  15. Cho, In-Koo & Kreps, David M, 1987. "Signaling Games and Stable Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 102(2), pages 179-221, May. [Downloadable!] (restricted)
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  27. Eddie Dekel & Drew Fudenberg & David K. Levine, 1996. "Payoff Information and Self-Confirming Equilibrium," Harvard Institute of Economic Research Working Papers 1774, Harvard - Institute of Economic Research.
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  28. Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May. [Downloadable!] (restricted)
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  35. L. G. Godfrey & A. R. Tremayne, 1998. "Reply," Econometric Reviews, Taylor and Francis Journals, vol. 7(1), pages 63-64. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  2. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics. [Downloadable!]
    Other versions:
  3. Faruk Gul & Wolfgang Pesendorfer, 2006. "The Canonical Type Space for Interdependent Preferences," Levine's Bibliography 321307000000000457, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. Barry O'Neill, 2006. "Nuclear Weapons and National Prestige," Cowles Foundation Discussion Papers 1560, Cowles Foundation, Yale University. [Downloadable!]
  5. Daisuke Oyama & Olivier Tercieux, 2007. "Robust Equilibria under Non-Common Priors," Levine's Bibliography 843644000000000210, UCLA Department of Economics. [Downloadable!]
    Other versions:
  6. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Cowles Foundation Discussion Papers 1421R, Cowles Foundation, Yale University, revised Apr 2004. [Downloadable!]
    Other versions:
  7. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Levine's Bibliography 122247000000001569, UCLA Department of Economics. [Downloadable!]
    Other versions:
  8. Dirk Bergemann & Stephen Morris, 2006. "Robust Implementation: The Case of Direct Mechanisms," Levine's Bibliography 122247000000001194, UCLA Department of Economics. [Downloadable!]
    Other versions:
  9. Pierpaolo Battigalli, . "Rationalization in Signaling Games: Theory and Applications," Working Papers 275, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
  10. Jonathan Weinstein & Muhamet Yildiz, 2004. "Finite-Order Implications of Any Equilibrium," Levine's Working Paper Archive 122247000000000065, UCLA Department of Economics. [Downloadable!]
  11. Eddie Dekel & Drew Fudenberg, 2006. "Topologies on Type," Discussion Papers 1417, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  12. Amanda Friedenberg, 2006. "Can Hidden Variables Explain Correlation? (joint with Adam Brandenburger)," Theory workshop papers 815595000000000005, UCLA Department of Economics. [Downloadable!]
  13. Hitoshi Matsushima, 2004. "On Detail-Free Mechanism Design and Rationality," CIRJE F-Series CIRJE-F-287, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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  14. Wolfgang Pesendorfer & Faruk Gul, 2007. "The Canonical Space for Behavioral Types," Levine's Bibliography 843644000000000345, UCLA Department of Economics. [Downloadable!]
  15. Dirk Bergemann & Stephen Morris, 2007. "The Role of the Common Prior in Robust Implementation," Levine's Bibliography 122247000000001574, UCLA Department of Economics. [Downloadable!]
    Other versions:
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