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Properties and applications of dual reduction

  • Yannick Viossat

    ()

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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File URL: http://hdl.handle.net/10.1007/s00199-009-0477-6
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Article provided by Springer in its journal Economic Theory.

Volume (Year): 44 (2010)
Issue (Month): 1 (July)
Pages: 53-68

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Handle: RePEc:spr:joecth:v:44:y:2010:i:1:p:53-68
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  1. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  2. Dhillon, A. & Mertens, J.F., . "Perfect correlated equilibria," CORE Discussion Papers RP -1197, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
  4. 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.
  5. Yannick Viossat, 2008. "Is Having a Unique Equilibrium Robust?," Post-Print hal-00361891, HAL.
  6. AUMANN, Robert J., . "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP -167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Viossat, Yannick, 2010. "Properties and applications of dual reduction," Economics Papers from University Paris Dauphine 123456789/882, Paris Dauphine University.
  8. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. 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).
  10. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
  11. 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.
  12. Robert Nau & Sabrina Gomez Canovas & Pierre Hansen, 2004. "On the geometry of Nash equilibria and correlated equilibria," International Journal of Game Theory, Springer, vol. 32(4), pages 443-453, 08.
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