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Stepwise Thinking in Strategic Games with Incomplete Information

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  • Carsten S. Nielsen

    (Department of Economics, University of Copenhagen)

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    Abstract

    This paper proposes a general incomplete information framework for studying behavior in strategic games with stepwise (viz. `level-k' or `cognitive hierarchy') thinking, which has been found to describe strategic behavior well in experiments involving players' initial responses to games. It is shown that there exist coherent stepwise beliefs, implied by step types, that have the potential to encode all relevant information. In the structure of stepwise beliefs, players are unaware of opponents doing at least as much thinking as themselves. As a result, there exists a Bayesian Nash equilibrium strategy profile in which any player at some step fixes the best responses of opponents at lower steps and then best responds herself.

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    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2010/1022.pdf/
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    Bibliographic Info

    Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 10-22.

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    Length: 27 pages
    Date of creation: Jul 2010
    Date of revision: Sep 2010
    Handle: RePEc:kud:kuiedp:1022

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    Related research

    Keywords: game theory; interactive epistemology; unawareness; Bayesian Nash equilibrium; bounded rationality; level-k; cognitive hierarchy;

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    1. Rosemarie Nagel & Antoni Bosch-Domènech & Albert Satorra & José García Montalvo, 1999. "One, two, (three), infinity: Newspaper and lab beauty-contest experiments," Economics Working Papers 438, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Miguel A. Costa-Gomes & Vincent P. Crawford, 2004. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," Levine's Bibliography 122247000000000113, UCLA Department of Economics.
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