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Properties and applications of dual reduction

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  • Yannick Viossat

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 strat- egies 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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Suggested Citation

  • Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    • Handle: RePEc:spr:joecth:v:44:y:2010:i:1:p:53-68
    DOI: 10.1007/s00199-009-0477-6
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    1. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
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    4. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    5. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    6. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    7. 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).
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    9. 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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    12. Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," SSE/EFI Working Paper Series in Economics and Finance 641, Stockholm School of Economics.
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    Cited by:

    1. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953, HAL.
    2. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
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    4. repec:dau:papers:123456789/882 is not listed on IDEAS
    5. Yohan Pelosse, 2024. "Correlated Equilibrium Strategies with Multiple Independent Randomization Devices," Working Papers 2024-05, Swansea University, School of Management.

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    More about this item

    Keywords

    Correlated equilibrium; Nash equilibrium; Dual reduction; Linear duality; C72;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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