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Properties and applications of dual reduction

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  • Yannick Viossat

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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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Bibliographic Info

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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Related research

Keywords: Correlated equilibrium; Nash equilibrium; Dual reduction; Linear duality; C72;

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References

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  1. Viossat, Yannick, 2008. "Is Having a Unique Equilibrium Robust?," Economics Papers from University Paris Dauphine 123456789/387, Paris Dauphine University.
  2. Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
  4. Dhillon, Amrita & Mertens, Jean Francois, 1996. "Perfect Correlated Equilibria," Journal of Economic Theory, Elsevier, vol. 68(2), pages 279-302, February.
  5. Yannick Viossat, 2010. "Properties and applications of dual reduction," Post-Print hal-00264031, HAL.
  6. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  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. R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
  9. 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.
  10. 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).
  11. 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.
  12. 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. Viossat, Yannick, 2004. "Replicator Dynamics and Correlated Equilibrium," Economics Papers from University Paris Dauphine 123456789/5219, Paris Dauphine University.
  2. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer, vol. 44(1), pages 53-68, July.

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