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

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  • Willemien Kets

Abstract

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: 22 Jul 2013
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Handle: RePEc:nwu:cmsems:1569

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Keywords: Bounded rationality; higher-order beliefs; finite depth of reasoning; games with incomplete information; Bayesian equilibrium JEL Classification: C700; C720; D800; D830;

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References

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  1. Miguel Costa-Gomes & Vincent P. Crawford & Bruno Broseta, . "Cognition and Behavior in Normal-Form Games:An Experimental Study," Discussion Papers 00/45, Department of Economics, University of York.
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  7. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
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  9. 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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Cited by:
  1. 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.

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