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The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games

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Author Info
Viossat, Yannick () (Dept. of Economics, Stockholm School of Economics)
Abstract

A pure strategy is coherent if it is played with positive probability in at least one correlated equilibrium. A game is pre-tight if in every correlated equilibrium, all incentives constraints for non deviating to a coherent strategy are tight. We show that there exists a Nash equilibrium in the relative interior of the correlated equilibrium polytope if and only if the game is pre-tight. Furthermore, the class of pre-tight games is shown to include and generalize the class of two-player zero-sum games.

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Publisher Info
Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 641.

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Length: 32 pages
Date of creation: 29 Aug 2006
Date of revision:
Handle: RePEc:hhs:hastef:0641

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Related research
Keywords: correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October. [Downloadable!] (restricted)
    Other versions:
  2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March. [Downloadable!] (restricted)
  3. Sergiu Hart, 2005. "Adaptive Heuristics," Econometrica, Econometric Society, vol. 73(5), pages 1401-1430, 09. [Downloadable!] (restricted)
    Other versions:
  4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-28, July. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515, March.
  7. 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. [Downloadable!]
  8. Evangelista, Fe S & Raghavan, T E S, 1996. "A Note on Correlated Equilibrium," International Journal of Game Theory, Springer, vol. 25(1), pages 35-41.
  9. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
  11. Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
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