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Hierarchies of belief and interim rationalizability

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Author Info

  • Ely, Jeffrey C.

    ()
    (Northwestern University)

  • Peski, Marcin

    ()
    (University of Chicago)

Abstract

In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players' information for the purposes of determining a player's behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player's information to identify behavior. We specialize to two player games and the solution concept of interim rationalizability. We construct the universal type space for rationalizability and characterize the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs , which we call Delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same Delta-hierarchies.

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Bibliographic Info

Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): 1 (2006)
Issue (Month): 1 (March)
Pages: 19-65

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Handle: RePEc:the:publsh:163

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Web page: http://econtheory.org

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Keywords: Interim rationalizability; belief hierarchies;

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  1. 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.
  2. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
  3. R. Aumann, 2010. "Correlated Equilibrium as an expression of Bayesian Rationality," Levine's Bibliography 513, UCLA Department of Economics.
  4. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December.
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