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Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information

  • Willemien Kets

The standard framework for analyzing games with incomplete information models players as if they have an infinite depth of reasoning, which is not always consistent with experimental evidence. This paper generalizes the type spaces of Harsanyi (1967- 1968) so that players can have a nite depth of reasoning. We do this restricting the set of events that a player of a finite depth can reason about. This approach allows us to extend the Bayesian-Nash equilibrium concept to environments with players with a nite depth of reasoning. We demonstrate that the standard approach of modeling beliefs with Harsanyi type spaces fails to capture the equilibrium behavior of players with a nite depth, at least in some games. Consequently, the standard approach cannot be used to describe the equilibrium behavior of players with a finite depth in general.

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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 1569.

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Date of creation: 07 Feb 2014
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Handle: RePEc:nwu:cmsems:1569
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  1. 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.
  2. Eddie Dekel & Drew Fudenberg & David K Levine, 2002. "Learning to Play Bayesian Games," Levine's Working Paper Archive 625018000000000151, David K. Levine.
  3. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
  4. Strzalecki, Tomasz, 2014. "Depth of reasoning and higher order beliefs," Journal of Economic Behavior & Organization, Elsevier, vol. 108(C), pages 108-122.
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  7. Costa-Gomes, Miguel & Crawford, Vincent P & Broseta, Bruno, 2001. "Cognition and Behavior in Normal-Form Games: An Experimental Study," Econometrica, Econometric Society, vol. 69(5), pages 1193-1235, September.
  8. Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006. "Topologies on Types," Scholarly Articles 3160489, Harvard University Department of Economics.
  9. Crawford, Vincent P. & Iriberri, Nagore, 2005. "Level-k Auctions: Can a Non-Equilibrium Model of Strategic Thinking Explain the Winner's Curse and Overbidding in Private-Value Auctions?," University of California at San Diego, Economics Working Paper Series qt12586197, Department of Economics, UC San Diego.
  10. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  11. 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.
  12. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-91, June.
  14. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  15. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  16. Ho, Teck Hua & Weigelt, Keith & Camerer, Colin, 1996. "Iterated Dominance and Iterated Best-Response in Experimental P-Beauty Contests," Working Papers 974, California Institute of Technology, Division of the Humanities and Social Sciences.
  17. 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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