All Types Naive and Canny
AbstractThis 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
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1550.
Date of creation: 04 Aug 2012
Date of revision:
Contact details of provider:
Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Web page: http://www.kellogg.northwestern.edu/research/math/
More information through EDIRC
Find related papers by JEL classification:
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-09-09 (All new papers)
- NEP-GTH-2012-09-09 (Game Theory)
- NEP-MIC-2012-09-09 (Microeconomics)
- NEP-NEU-2012-09-09 (Neuroeconomics)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Monderer, Dov & Samet, Dov, 1989. "Approximating common knowledge with common beliefs," Games and Economic Behavior, Elsevier, vol. 1(2), pages 170-190, June.
- Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
- Di Tillio, Alfredo, 2008.
"Subjective expected utility in games,"
Econometric Society, vol. 3(3), September.
- Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2005.
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.
- Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
- Aviad Heifetz & Dov Samet, 1996.
"Topology-Free Typology of Beliefs,"
Game Theory and Information
9609002, EconWPA, revised 17 Sep 1996.
- Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
- Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
- Carlsson, H. & Damme, E.E.C. van, 1990.
"Global games and equilibrium selection,"
1990-52, Tilburg University, Center for Economic Research.
- Carlsson, H. & Van Damme, E., 1990. "Global Games And Equilibrium Selection," Papers 9052, Tilburg - 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. & Damme, E.E.C. van, 1993. "Global games and equilibrium selection," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154416, Tilburg University.
- Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
- Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
- Tomasz Strzalecki, 1969. "Depth of Reasoning and Higher Order Beliefs," Working Paper 8334, Harvard University OpenScholar.
- Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
- Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
- Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jayant V. Ganguli & Aviad Heifetz, 2012. "Universal interactive preferences," Economics Discussion Papers 722, University of Essex, Department of Economics.
- Willemien Kets, 2013. "Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information," Discussion Papers 1569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fran Walker).
If references are entirely missing, you can add them using this form.