On the Structure of Rationalizability for Arbitrary Spaces of Uncertainty

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On the Structure of Rationalizability for Arbitrary Spaces of Uncertainty

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Antonio Penta () (Department of Economics, University of Pennsylvania)

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Antonio Penta

Abstract

This note characterizes the set A¡∞ of actions of player ¡ that are uniquely rationalizable for some hierarchy of beliefs on an arbitrary space of uncertainty. It is proved that for any rationalizable action a¡ for the type t¡, if a¡ belongs to A¡∞ and is justified by conjectures concentrated on A-¡∞, then there exists a sequence of types converging to t¡ for which a¡ is uniquely rationalizable.

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Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 09-021.

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Length: 12 pages
Date of creation: 01 Oct 2008
Date of revision: 05 Jun 2008
Handle: RePEc:pen:papers:09-021

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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
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Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
Ely, Jeffrey C. & Peski, Marcin, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Society for Economic Theory, vol. 1(1), pages 19-65, March. [Downloadable!]
Other versions:
- Jeffrey C. Ely & Marcin Peski, 2005. "Hierarchies of Belief and Interim Rationalizability," Levine's Bibliography 122247000000000817, UCLA Department of Economics. [Downloadable!]
- 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. [Downloadable!]
Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)

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