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How to Use Decision Theory to Choose Among Mechanisms

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  • James W. Bono
  • David H. Wolpert

Abstract

We extend a recently introduced approach to the positive problem of game theory, Predictive Game Theory (PGT Wolpert (2008). In PGT, modeling a game results in a probability distribution over possible behavior profiles. This contrasts with the conventional approach where modeling a game results in an equilibrium set of possible behavior profiles. We analyze three PGT models. Two of these are based on the well-known quantal response and epsilon equilibrium concepts, while the third is entirely new to the economics literature. We use a Cournot game to demonstrate how to use our extension of PGT, concentrating on model combination, modeler uncertainty, and mechanism design. In particular, we emphasize how PGT allows a modeler to perform prediction and mechanism design in a manner that is fully consistent with decision theory. We do this even in situations where conventional approaches yield multiple equilibria, an ability that is necessary for a fully decision theoretic mechanism design. Where possible, PGT results are compared against equilibrium set analogs.

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File URL: http://www.american.edu/cas/economics/pdf/upload/working-paper-11-bono-and-wolpert.pdf
File Function: First version, 2009
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Bibliographic Info

Paper provided by American University, Department of Economics in its series Working Papers with number 2009-11.

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Date of creation: Aug 2009
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Handle: RePEc:amu:wpaper:2009-11

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

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  1. 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.
  2. Harsanyi, John C., 1994. "Games with Incomplete Information," Nobel Prize in Economics documents 1994-1, Nobel Prize Committee.
  3. Seade, J, 1985. "Profitable Cost Increases and the Shifting of Taxation : Equilibrium Response of Markets in Oligopoly," The Warwick Economics Research Paper Series (TWERPS) 260, University of Warwick, Department of Economics.
  4. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-11, May.
  5. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
  6. 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. Velu, C. & Iyer, S. & Gair, J.R., 2010. "A Reason for Unreason: Returns-Based Beliefs in Game Theory," Cambridge Working Papers in Economics 1058, Faculty of Economics, University of Cambridge.

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