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Properties and applications of dual reduction

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  • Yannick Viossat

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Yannick Viossat, 2010. "Properties and applications of dual reduction," Post-Print hal-00264031, HAL.
    • Handle: RePEc:hal:journl:hal-00264031
    DOI: 10.1007/s00199-009-0477-6
    Note: View the original document on HAL open archive server: https://hal.science/hal-00264031v2
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    References listed on IDEAS

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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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    3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    4. Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
    5. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 133-154.
    6. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    7. 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.
    8. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    10. Robert Nau & Sabrina Gomez Canovas & Pierre Hansen, 2004. "On the geometry of Nash equilibria and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 443-453, August.
    11. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759, Elsevier.
    12. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    13. 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).
    14. 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..
    15. 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..
    16. Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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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

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    More about this item

    Keywords

    correlated equilibrium; Nash equilibrium; dual reduction; équilibre corrélé; équilibre de Nash; réduction duale;
    All these keywords.

    JEL classification:

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

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