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 all strat- egies 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, Economic Theory, 2010, 44, 53--68|
|Note:||View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00264031|
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- Dhillon, A. & Mertens, J.F., .
"Perfect correlated equilibria,"
CORE Discussion Papers RP
-1197, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hofbauer, Josef & Weibull, Jîrgen W., 1995.
"Evolutionary selection against dominated strategies,"
CEPREMAP Working Papers (Couverture Orange)
- Hofbauer, Josef & Weibull, Jorgen W., 1996. "Evolutionary Selection against Dominated Strategies," Journal of Economic Theory, Elsevier, vol. 71(2), pages 558-573, November.
- J. Hofbauer & J. Weibull, 2010. "Evolutionary Selection against dominated strategies," Levine's Working Paper Archive 444, David K. Levine.
- Hofbauer, Josef & Weibull, Jörgen W., 1995. "Evolutionary Selection against Dominated Strategies," Working Paper Series 433, Research Institute of Industrial Economics.
- Viossat, Yannick, 2010.
"Properties and applications of dual reduction,"
Economics Papers from University Paris Dauphine
123456789/882, Paris Dauphine University.
- Yannick Viossat, 2008.
"Is Having a Unique Equilibrium Robust?,"
- 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.
- 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).
- 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.
- Myerson, Roger B., 1997.
"Dual Reduction and Elementary Games,"
Games and Economic Behavior,
Elsevier, vol. 21(1-2), pages 183-202, October.
- 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.
- 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.
- 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).
- KOHLBERG, Elon & MERTENS, Jean-François, .
"On the strategic stability of equilibria,"
CORE Discussion Papers RP
-716, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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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