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

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  • 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.

Suggested Citation

  • 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.
  • Handle: RePEc:hhs:hastef:0641
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    File URL: http://swopec.hhs.se/hastef/papers/hastef0641.pdf
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    References listed on IDEAS

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    1. 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.
    2. Myerson, Roger B., 1997. "Dual Reduction and Elementary Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 183-202, October.
    3. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    4. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    5. Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
    6. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters,in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287 World Scientific Publishing Co. Pte. Ltd..
    7. Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515-515, March.
    8. Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    9. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    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. Evangelista, Fe S & Raghavan, T E S, 1996. "A Note on Correlated Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(1), pages 35-41.
    12. Robert Nau & Sabrina Gomez Canovas & Pierre Hansen, 2004. "On the geometry of Nash equilibria and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 443-453, August.
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    Cited by:

    1. Yannick Viossat, 2010. "Properties and applications of dual reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 53-68, July.
    2. Robert Nau, 2015. "Risk-neutral equilibria of noncooperative games," Theory and Decision, Springer, vol. 78(2), pages 171-188, February.
    3. repec:wsi:igtrxx:v:20:y:2018:i:03:n:s0219198918400017 is not listed on IDEAS
    4. repec:dau:papers:123456789/882 is not listed on IDEAS

    More about this item

    Keywords

    correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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