Abstract
The dual reduction process, introduced by Myerson, allows a finite game to be reduced to a smaller-dimensional game such that any correlated equilibrium of the reduced game is an equilibrium of the original game. We study the properties and applications of this process. It is shown that generic two-player normal form games have a unique full dual reduction (a known refinement of dual reduction) and all strategies that have probability zero in all correlated equilibria are eliminated in all full dual reductions. Among other applications, we give a linear programming proof of the fact that a unique correlated equilibrium is a Nash equilibrium, and improve on a result due to Nau, Gomez-Canovas and Hansen on the geometry of Nash equilibria and correlated equilibria.
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This article originated in my Ph.D. thesis, written at the laboratoire d’économétrie de l’Ecole polytechnique, under the supervision of Sylvain Sorin. I am deeply grateful to Bernhard von Stengel and to Françoise Forges, Ehud Lehrer, Roger Myerson, seminar audiences, and several anonymous referees whose constructive comments helped me to improve the presentation of this article. All shortcomings are mine. The author gratefully acknowledges the support of the ANR, project “Croyances” and of the Fondation du Risque, Chaire Groupama, “Les particuliers face au risque”.
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Viossat, Y. Properties and applications of dual reduction. Econ Theory 44, 53–68 (2010). https://doi.org/10.1007/s00199-009-0477-6
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DOI: https://doi.org/10.1007/s00199-009-0477-6