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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)

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.

Suggested Citation

  • Carsten S. Nielsen, 2010. "Stepwise Thinking in Strategic Games with Incomplete Information," Discussion Papers 10-22, University of Copenhagen. Department of Economics, revised Sep 2010.
    • Handle: RePEc:kud:kuiedp:1022
    as

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    File URL: http://www.econ.ku.dk/english/research/publications/wp/dp_2010/1022.pdf/
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    References listed on IDEAS

    as
    1. Antoni Bosch-Domènech & José G. Montalvo & Rosemarie Nagel & Albert Satorra, 2002. "One, Two, (Three), Infinity, ...: Newspaper and Lab Beauty-Contest Experiments," American Economic Review, American Economic Association, vol. 92(5), pages 1687-1701, December.
    2. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
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    More about this item

    Keywords

    game theory; interactive epistemology; unawareness; Bayesian Nash equilibrium; bounded rationality; level-k; cognitive hierarchy;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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