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Properties of Dual Reduction

  • Yannick Viossat

    (CECO - Laboratoire d'econometrie de l'école polytechnique - CNRS - Polytechnique - X)

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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Date of creation: 2003
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Handle: RePEc:hal:wpaper:hal-00242992
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  1. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  2. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
    • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
  3. Yannick Viossat, 2003. "Geometry, Correlated Equilibria and Zero-Sum Games," Working Papers hal-00242993, HAL.
  4. 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.
  5. Myerson, R B, 1986. "Acceptable and Predominant Correlated Equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 15(3), pages 133-54.
  6. Dhillon, A. & Mertens, J.F., . "Perfect correlated equilibria," CORE Discussion Papers RP 1197, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. 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).
  9. S. Sorin, 1998. "Distribution equilibrium I : Definition and examples," THEMA Working Papers 98-35, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  10. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, 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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