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Properties and applications of dual reduction

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  • Viossat, Yannick

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 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.

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Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/882.

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Date of creation: 2010
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Publication status: Published in Economic Theory, 2010, Vol. 44, no. 1. pp. 53-68.Length: 15 pages
Handle: RePEc:dau:papers:123456789/882

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Keywords: Linear duality; Dual reduction; Nash equilibrium; Correlated equilibrium; Théorie des jeux;

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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, 2008. "Is Having a Unique Equilibrium Robust?," Post-Print, HAL hal-00361891, HAL.
  3. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(2), pages 424-444, April.
  4. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 21(1-2), pages 183-202, October.
  6. Dhillon, A. & Mertens, J.F., . "Perfect correlated equilibria," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1197, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, Econometric Society, vol. 54(5), pages 1003-37, September.
  8. Viossat, Yannick, 2006. "The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games," Working Paper Series in Economics and Finance 641, Stockholm School of Economics.
  9. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer, Springer, vol. 44(1), pages 53-68, July.
  10. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
  11. Robert Nau & Sabrina Gomez Canovas & Pierre Hansen, 2004. "On the geometry of Nash equilibria and correlated equilibria," International Journal of Game Theory, Springer, Springer, vol. 32(4), pages 443-453, 08.
  12. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
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Cited by:
  1. Yannick Viossat, 2004. "Replicator Dynamics and Correlated Equilibrium," Working Papers hal-00242953, HAL.
  2. Viossat, Yannick, 2010. "Properties and applications of dual reduction," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/882, Paris Dauphine University.

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