Refined best reply correspondence and dynamics
We call a correspondence, defined on the set of mixed strategy profiles, a generalized best reply correspondence if it has (1) a product structure, is (2) upper semi-continuous, (3) always includes a best reply to any mixed strategy profile, and is (4) convex- and closed-valued. For each generalized best reply correspondence we define a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profiles a minimally asymptotically stable face (MASF) if it is asymptotically stable under some such dynamics and no subface of it is asymptotically stable under any such dynamics. The set of such correspondences (and dynamics) is endowed with the partial order of point-wise set-inclusion and, under a mild condition on the normal form of the game at hand, forms a complete lattice with meets based on point-wise intersections. The refined best reply correspondence is then defined as the smallest element of the set of all generalized best reply correspondences. We ultimately find that every Kalai and Samet's (1984) persistent retract, which coincide with Basu and Weibull's (1991) CURB sets based, however, on the refined best reply correspondence, contains a MASF. Conversely, every MASF must be a Voorneveld's (2004) prep set, again, however, based on the refined best reply correspondence.
|Date of creation:||Jul 2011|
|Date of revision:|
|Contact details of provider:|| Postal: Postfach 10 01 31, 33501 Bielefeld|
Web page: http://www.imw.uni-bielefeld.de/
More information through EDIRC
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.:
- van Damme, E.E.C. & Hurkens, J.P.M., 1993.
"Commitment robust equilibria and endogenous timing,"
1993-56, Tilburg University, Center for Economic Research.
- van Damme, Eric & Hurkens, Sjaak, 1996. "Commitment Robust Equilibria and Endogenous Timing," Games and Economic Behavior, Elsevier, vol. 15(2), pages 290-311, August.
- van Damme, E.E.C. & Hurkens, J.P.M., 1996. "Commitment robust equilibria and endogenous timing," Other publications TiSEM ec7a3425-4254-44da-8ef4-e, Tilburg University, School of Economics and Management.
- Van Damme, E. & Hurkens, S., 1993. "Commitment Robust Equilibria and Endogenous Timing," Papers 9356, Tilburg - Center for Economic Research.
- Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
- Blume, A., 1992.
"Equilibrium Refinements in Sender-Receiver Games,"
92-12, University of Iowa, Department of Economics.
- Dekel, Eddie & Fudenberg, Drew, 1990.
"Rational behavior with payoff uncertainty,"
Journal of Economic Theory,
Elsevier, vol. 52(2), pages 243-267, December.
- Balkenborg, Dieter & Hofbauer, Josef & Kuzmics, Christoph, 2014. "The refined best-response correspondence in normal form games," Center for Mathematical Economics Working Papers 466, Center for Mathematical Economics, Bielefeld University.
- Kohlberg, Elon & Mertens, Jean-Francois, 1986.
"On the Strategic Stability of Equilibria,"
Econometric Society, vol. 54(5), pages 1003-37, September.
- 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).
- E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
- Kets, Willemien & Voorneveld, Mark, 2005.
"Learning to be prepared,"
SSE/EFI Working Paper Series in Economics and Finance
590, Stockholm School of Economics.
- Ritzberger, Klaus & Weibull, Jorgen W, 1995.
"Evolutionary Selection in Normal-Form Games,"
Econometric Society, vol. 63(6), pages 1371-99, November.
- Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Itzhak Gilboa & Akihiko Matsui, 1991.
"Social Stability and Equilibrium,"
- Balkenborg, D. & Jansen, M. & Vermeulen, D., 1998.
"Invariance properties of persistent equilibria and related solution concepts,"
Discussion Paper Series In Economics And Econometrics
9806, Economics Division, School of Social Sciences, University of Southampton.
- Balkenborg, Dieter & Jansen, Mathijs & Vermeulen, Dries, 2001. "Invariance properties of persistent equilibria and related solution concepts," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 111-130, January.
- Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, June.
- Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
- Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
- Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
- Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, June.
- Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, July.
- Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
When requesting a correction, please mention this item's handle: RePEc:bie:wpaper:451. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bettina Weingarten)
If references are entirely missing, you can add them using this form.