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All Types Naive and Canny

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  • Aviad Heifetz
  • Willemien Kets

Abstract

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

Suggested Citation

  • Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1550
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1547.pdf
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    References listed on IDEAS

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    1. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
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    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. 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..
    5. Di Tillio, Alfredo, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
    6. 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.
    7. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    8. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    9. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    10. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
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    12. Ahn, David S., 2007. "Hierarchies of ambiguous beliefs," Journal of Economic Theory, Elsevier, vol. 136(1), pages 286-301, September.
    13. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
    14. 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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    16. Robert J Aumann, 1999. "Agreeing to Disagree," Levine's Working Paper Archive 512, David K. Levine.
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    Citations

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    Cited by:

    1. Heifetz, Aviad & Kets, Willemien, 2018. "Robust multiplicity with a grain of naiveté," Theoretical Economics, Econometric Society, vol. 13(1), January.
    2. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    3. Ganguli, Jayant & Heifetz, Aviad & Lee, Byung Soo, 2016. "Universal interactive preferences," Journal of Economic Theory, Elsevier, vol. 162(C), pages 237-260.
    4. repec:esx:essedp:722 is not listed on IDEAS
    5. Willemien Kets, 2014. "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.
    6. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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    Keywords

    Level-k models; cognitive hierarchy models; universal type space; global games;

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