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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.

Suggested Citation

  • James W. Bono & David H. Wolpert, 2009. "How to Use Decision Theory to Choose Among Mechanisms," Working Papers 2009-11, American University, Department of Economics.
  • Handle: RePEc:amu:wpaper:2009-11
    DOI: 10.17606/x0xa-4222
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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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