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.
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- K. Ritzberger & J. Weibull, 2010.
"Evolutionary Selection in Normal-Form Games,"
Levine's Working Paper Archive
452, David K. Levine.
- 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).
- Ehud Kalai & Dov Samet, 1982. "Persistent Equilibria in Strategic Games," Discussion Papers 515, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, December.
- Blume, A., 1991.
"Equilibrium Refinement in Sender-Receiver Games,"
91-28, University of Iowa, Department of Economics.
- Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
- Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
- 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.E.C. & Hurkens, J.P.M., 1993. "Commitment robust equilibria and endogenous timing," Discussion Paper 1993-56, Tilburg University, Center for Economic Research.
- Van Damme, E. & Hurkens, S., 1993. "Commitment Robust Equilibria and Endogenous Timing," Papers 9356, Tilburg - Center for Economic Research.
- Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, December.
- Basu, Kaushik & Weibull, Jorgen W., 1991.
"Strategy subsets closed under rational behavior,"
Elsevier, vol. 36(2), pages 141-146, June.
- Drew Fudenberg & Eddie Dekel, 1987.
"Rational Behavior with Payoff Uncertainty,"
471, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- I. Gilboa & A. Matsui, 2010.
"Social Stability and Equilibrium,"
Levine's Working Paper Archive
534, David K. Levine.
- Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
- 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.
- Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2015. "The refined best-response correspondence in normal form games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 165-193, February.
- Hurkens Sjaak, 1995. "Learning by Forgetful Players," Games and Economic Behavior, Elsevier, vol. 11(2), pages 304-329, November.
- 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.
- Kets, Willemien & Voorneveld, Mark, 2005.
"Learning to be prepared,"
SSE/EFI Working Paper Series in Economics and Finance
590, Stockholm School of Economics.
- 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.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
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