Refined best-response correspondence and dynamics
We call a correspondence, defined on the set of mixed strategy pro les, a generalized best reply correspondence if it (1) has a product structure, (2) is upper hemi-continuous, (3) always includes a best reply to any mixed strategy pro le, and (4) is convex- and closed-valued. For each generalized best reply correspondence, we defi ne a generalized best reply dynamics as a differential inclusion based on it. We call a face of the set of mixed strategy profi les 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 find that every persistent retract (Kalai and Samet 1984) contains an MASF. Furthermore, persistent retracts are minimal CURB sets (Basu and Weibull 1991) based on the refi ned best reply correspondence. Conversely, every MASF must be a prep set (Voorneveld 2004), based again, however, on the refined best reply correspondence.
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.:
- 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.
- 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.
- von Stengel, Bernhard & Zamir, Shmuel, 2010.
"Leadership games with convex strategy sets,"
Games and Economic Behavior,
Elsevier, vol. 69(2), pages 446-457, July.
- Bernhard von Stengel & Shmuel Zamir, 2010. "Leadership games with convex strategy sets," LSE Research Online Documents on Economics 27653, London School of Economics and Political Science, LSE Library.
- Bernhard von Stengel & Shmuel Zamir, 2009. "Leadership Games with Convex Strategy Sets," Discussion Paper Series dp525, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Dieter Balkenborg & Josef Hofbauer & Christoph Kuzmics, 2012. "The refined best-response correspondence in normal form games," Working Papers 466, Bielefeld University, Center for Mathematical Economics.
- 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.
- Kets, W. & Voorneveld, M., 2005.
"Learning to be Prepared,"
2005-117, Tilburg University, Center for Economic Research.
- Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, June.
- Michel Benaïm & Josef Hofbauer & Sylvain Sorin, 2003. "Stochastic Approximations and Differential Inclusions," Working Papers hal-00242990, HAL.
- S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
- Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868.
- Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
- Sergiu Hart & Andreu Mas-Colell, 2002. "Uncoupled dynamics cannot lead to Nash equilibrium," Discussion Paper Series dp299, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
When requesting a correction, please mention this item's handle: RePEc:the:publsh:652. 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: (Martin J. Osborne)
If references are entirely missing, you can add them using this form.