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Distribution-Valued Solution Concepts

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  • David H. Wolpert
  • James Bono

Abstract

Under its conventional positive interpretation, game theory predicts that the mixed strategy pro?le of players in a noncooperative game will satisfy some setvalued solution concept. Relative probabilities of pro?les in that set are unspeci?ed, and all pro?les not satisfying it are implicitly assigned probability zero. However the axioms underlying Bayesian rationality say that we should reason about player behavior using a probability density over all mixed strategy pro?les, not using a subset of all such pro?les. Such a density over pro?les can be viewed as a solution concept that is distribution-valued rather than set-valued. A distribution-valued concept provides a best single prediction for any noncooperative game, i.e., a universal re?nement. In addition, regulators can use a distribution-valued solution concept to make Bayes optimal choices of a mechanism, as required by Savage's axioms. In particular, they can do this in strategic situations where conventional mechanism design cannot provide advice. We illustrate all of this on a Cournot duopoly game.

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File URL: http://www.american.edu/cas/economics/pdf/upload/2010-13.pdf
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Bibliographic Info

Paper provided by American University, Department of Economics in its series Working Papers with number 2010-13.

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Date of creation: Jun 2010
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Handle: RePEc:amu:wpaper:2010-13

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Web page: http://www.american.edu/cas/economics/

Related research

Keywords: Quantal Response Equilibrium; Bayesian Statistics; Entropic prior; Maximum entropy JEL Codes: C02; C11; C70; C72;

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  1. Miguel Costa-Gomes & Vincent P. Crawford, 2004. "Cognition And Behavior In Two-Person Guessing Games: An Experimental Study," Levine's Bibliography 122247000000000143, UCLA Department of Economics.
  2. Pedro Mira & Victor Aguirregabiria, 2007. "Dynamic Discrete Choice Structural Models: A Survey," Working Papers wp2007_0711, CEMFI.
  3. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, MIT Press, vol. 119(3), pages 861-898, August.
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Cited by:
  1. David H. Wolpert & James Bono, 2010. "A theory of unstructured bargaining using distribution-valued solution concepts," Working Papers 2010-14, American University, Department of Economics.

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