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Hierarchies Of Belief And Interim Rationalizability

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JEFFREY C. ELY
MARCIN PESKI

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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 rationalizable behavior in any game. We do this by constructing the universal type space for rationalizability and characterizing the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, what 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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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1388.

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Handle: RePEc:nwu:cmsems:1388

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  1. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January. [Downloadable!] (restricted)
  2. 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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  3. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  1. Dirk Bergemann & Stephen Morris, 2007. "Belief Free Incomplete Information Games," Levine's Bibliography 122247000000001569, UCLA Department of Economics. [Downloadable!]
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  2. Pierpaolo Battigalli, . "Rationalization in Signaling Games: Theory and Applications," Working Papers 275, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
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  3. 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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  4. Wolfgang Pesendorfer & Faruk Gul, 2007. "The Canonical Space for Behavioral Types," Levine's Bibliography 843644000000000345, UCLA Department of Economics. [Downloadable!]
  5. Pierpaolo Battigalli & Alfredo Di Tillio & Edoardo Grillo & Antonio Penta, . "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," Working Papers 340, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University. [Downloadable!]
  6. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics. [Downloadable!]
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