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Properties and applications of dual reduction

Viossat, Yannick (2010), Properties and applications of dual reduction, Economic Theory, 44, 1, p. 53-68. http://dx.doi.org/10.1007/s00199-009-0477-6

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Economic Theory
Volume
44
Number
1
Publisher
Springer
Pages
53-68
Publication identifier
Metadata
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Author(s)
Viossat, Yannick
Abstract (EN)
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 that 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.
Subjects / Keywords
Linear duality; Dual reduction; Nash equilibrium; Correlated equilibrium; Théorie des jeux
JEL
C72 - Noncooperative Games