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Bounded Reasoning and Higher-Order Uncertainty

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  • Willemien Kets

Abstract

The standard framework for analyzing games with incomplete information models players as if they form beliefs about their opponents' beliefs about their opponents' beliefs and so on, that is, as if players have an infinite depth of reasoning. This strong assumption has nontrivial implications, as is well-known. This paper therefore generalizes the type spaces of Harsanyi (1967-1968) to model that players can have a finite depth of reasoning. The innovation is that players can have a coarse perception of the higher-order beliefs of other players, thus formalizing the small-world idea of Savage (1954) in a type-space context. Unlike the case in other models of finite-order reasoning, players with a finite depth of reasoning can have nontrivial higher-order beliefs about certain events. Intuitively, some higher-order events are generated by events of lower orders, making it possible for players to reason about them, even if they have a finite depth of reasoning.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1547.

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Date of creation: 19 Mar 2012
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Handle: RePEc:nwu:cmsems:1547

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References

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  6. Di Tillio, Alfredo, 2008. "Subjective expected utility in games," Theoretical Economics, Econometric Society, vol. 3(3), September.
  7. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  8. Heifetz, Aviad & Samet, Dov, 1998. "Knowledge Spaces with Arbitrarily High Rank," Games and Economic Behavior, Elsevier, vol. 22(2), pages 260-273, February.
  9. Brandenburger, Adam & Dekel, Eddie, 1987. "Common knowledge with probability 1," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 237-245, June.
  10. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
  11. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-26, December.
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  15. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Larbi Alaoui & Antonio Penta, 2014. "Endogenous Depth of Reasoning," Working Papers 653, Barcelona Graduate School of Economics.
  2. Jayant V. Ganguli & Aviad Heifetz, 2012. "Universal interactive preferences," Economics Discussion Papers 722, University of Essex, Department of Economics.
  3. 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.
  4. Davide Cianciaruso & Fabrizio Germano, 2011. "Quotient spaces of boundedly rational types," Economics Working Papers 1287, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Aviad Heifetz & Willemien Kets, 2013. "Robust Multiplicity with a Grain of Naiveté," Discussion Papers 1573, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.

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