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Properties of Dual Reduction

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  • Viossat, Yannick

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.

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File URL: http://basepub.dauphine.fr/xmlui/bitstream/123456789/3048/1/2005-06-07-956.pdf
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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/3048.

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Date of creation: 2003
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Publication status: Published in Cahiers du Laboratoire d'Econométrie, Ecole Polytechnique, 2003
Handle: RePEc:dau:papers:123456789/3048

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Related research

Keywords: Correlated Equilibria; Refinement; Réduction duale; Raffinement; Equilibres correlés;

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  1. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. DHILLON, Amrita & MERTENS, Jean-François, 1992. "Perfect correlated equilibria," CORE Discussion Papers 1992039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
  4. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer, vol. 15(3), pages 133-54.
  5. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. S. Sorin, 1998. "Distribution equilibrium I : Definition and examples," THEMA Working Papers 98-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  8. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  9. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Robert W. Rosenthal, 1973. "Correlated Equilibria in Some Classes of Two-Person Games," Discussion Papers 45, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
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Cited by:
  1. Yannick Viossat, 2003. "Elementary Games and Games Whose Correlated Equilibrium Polytope Has Full Dimension," Working Papers hal-00242991, HAL.
  2. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.

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