Hierarchies of Belief and Interim Rationalizability
AbstractIn games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the playersâ information for the purposes of determining a playerâs behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a playerâs 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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Bibliographic InfoPaper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000817.
Date of creation: 04 Jan 2005
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Other versions of this item:
- Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
- Jeffrey C. Ely & Marcin Peski, . "Hierarchies Of Belief And Interim Rationalizability," Discussion Papers 1388, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
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