Properties and applications of dual reduction
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.
|Date of creation:||2010|
|Date of revision:|
|Publication status:||Published in Economic Theory, 2010, Vol. 44, no. 1. pp. 53-68.Length: 15 pages|
|Contact details of provider:|| Web page: http://www.dauphine.fr/en/welcome.html|
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- Yannick Viossat, 2010.
"Properties and applications of dual reduction,"
- Dhillon, A. & Mertens, J.F., .
"Perfect correlated equilibria,"
CORE Discussion Papers RP
1197, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- J. Hofbauer & J. Weibull, 2010.
"Evolutionary Selection against dominated strategies,"
Levine's Working Paper Archive
444, David K. Levine.
- Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
- Hofbauer, Josef & Weibull, Jörgen W., 1995. "Evolutionary Selection against Dominated Strategies," Working Paper Series 433, Research Institute of Industrial Economics.
- Hofbauer, Josef & Weibull, Jîrgen W., 1995. "Evolutionary selection against dominated strategies," CEPREMAP Working Papers (Couverture Orange) 9506, CEPREMAP.
- 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.
- Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
- 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.
- Kohlberg, Elon & Mertens, Jean-Francois, 1986.
"On the Strategic Stability of Equilibria,"
Econometric Society, vol. 54(5), pages 1003-37, September.
- E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
- KOHLBERG, Elon & MERTENS, Jean-FranÃ§ois, . "On the strategic stability of equilibria," CORE Discussion Papers RP 716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Yannick Viossat, 2008.
"Is Having a Unique Equilibrium Robust?,"
- Roger B. Myerson, 1995.
"Dual Reduction and Elementary Games,"
1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Aumann, Robert J., 1974.
"Subjectivity and correlation in randomized strategies,"
Journal of Mathematical Economics,
Elsevier, vol. 1(1), pages 67-96, March.
- R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
- 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).
- MERTENSÂ , Jean-FranÃ§ois & SORINÂ , Sylvain & ZAMIRÂ , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
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