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Properties of Dual Reduction

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  • Yannick Viossat

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

We study dual reduction: a technique to reduce finite games in a way that selects among correlated equilibria. We show that the reduction process is independent of the utility functions chosen to represent the agents's preferences and that generic two-player games have a unique full dual reduction. Moreover, in full dual reductions, all strategies and strategy profiles which are never played in correlated equilibria are eliminated. The additional properties of dual reduction in several classes of games are studied and dual reduction is compared to other correlated equilibrium refinement's concepts. Finally, we review and connect the linear programming proofs of existence of correlated equilibria.

Suggested Citation

  • Yannick Viossat, 2003. "Properties of Dual Reduction," Working Papers hal-00242992, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242992
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242992
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    References listed on IDEAS

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    1. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    2. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
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    11. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," LIDAM Discussion Papers CORE 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
    13. Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
    2. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.

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