All Types Naive and Canny
This paper constructs a type space that contains all types with a finite depth of reasoning, as well as all types with an infinite depth of reasoning - in particular those types for whom finite-depth types are conceivable, or think that infnite-depth types are conceivable in the mind of other players, etcetera. We prove that this type space is uni- versal with respect to the class of type spaces that include types with a finite or infinite depth of reasoning. In particular, we show that it contains the standard universal type space of Mertens and Zamir (1985) as a belief-closed subspace, and that this subspace is characterized by common belief of infinite-depth reasoning. This framework allows us to study the robustness of classical results to small deviations from perfect rationality. As an example, we demonstrate that in the global games of Carlsson and van Damme (1993), a small ‘grain of naivete’ suffices to overturn the classical uniqueness results in that literature. JEL Code: C700, C720, D800, D830
|Date of creation:||04 Aug 2012|
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- Carlsson, Hans & van Damme, Eric, 1993.
"Global Games and Equilibrium Selection,"
Econometric Society, vol. 61(5), pages 989-1018, September.
- Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Discussion Paper 1990-52, Tilburg University, Center for Economic Research.
- Hans Carlsson & Eric van Damme, 1993. "Global Games and Equilibrium Selection," Levine's Working Paper Archive 122247000000001088, David K. Levine.
- Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
- Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - Center for Economic Research.
- Aviad Heifetz & Dov Samet, 1996.
"Topology-Free Typology of Beliefs,"
Game Theory and Information
9609002, EconWPA, revised 17 Sep 1996.
- Adam Brandenburger & Eddie Dekel, 2014.
"Hierarchies of Beliefs and Common Knowledge,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41
World Scientific Publishing Co. Pte. Ltd..
- Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
- Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
- Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006.
Journal of Economic Theory,
Elsevier, vol. 130(1), pages 78-94, September.
- HEIFETZ, Aviad & MEIER, Martin & SCHIPPER, Burkhard C., 2004. "Interactive unawareness," CORE Discussion Papers 2004059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2005. "Interactive Unawareness," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 52, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
- Amanda Friedenberg & Martin Meier, 2011. "On the relationship between hierarchy and type morphisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(3), pages 377-399, April.
- Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Strzalecki, Tomasz, 2014.
"Depth of reasoning and higher order beliefs,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 108(C), pages 108-122.
- Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
- Di Tillio, Alfredo, 2008.
"Subjective expected utility in games,"
Econometric Society, vol. 3(3), September.
- Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
- Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
- Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
- Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
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