The Geometry of Nash Equilibria and Correlated Equilibria and a Generalization of Zero-Sum Games
AbstractA 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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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 641.
Length: 32 pages
Date of creation: 29 Aug 2006
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More information through EDIRC
correlated equilibrium; Nash equilibrium; zero-sum games; dual reduction;
Find related papers by JEL classification:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-12-09 (All new papers)
- NEP-GTH-2006-12-09 (Game Theory)
- NEP-MIC-2006-12-09 (Microeconomics)
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.:
- R. Aumann, 2010.
"Subjectivity and Correlation in Randomized Strategies,"
Levine's Working Paper Archive
389, David K. Levine.
- Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
- Sergiu Hart, 2005.
Econometric Society, vol. 73(5), pages 1401-1430, 09.
- Bernheim, B Douglas, 1984.
"Rationalizable Strategic Behavior,"
Econometric Society, vol. 52(4), pages 1007-28, July.
- Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
- Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515, March.
- Myerson, Roger B., 1997.
"Dual Reduction and Elementary Games,"
Games and Economic Behavior,
Elsevier, vol. 21(1-2), pages 183-202, October.
- 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.
- 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.
- 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.
- Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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.
- repec:ner:dauphi:urn:hdl:123456789/171 is not listed on IDEAS
- Yannick Viossat, 2010.
"Properties and applications of dual reduction,"
Springer, vol. 44(1), pages 53-68, July.
- repec:ner:dauphi:urn:hdl:123456789/882 is not listed on IDEAS
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