Refined best-response correspondence and dynamics
We characterize the smallest faces of the polyhedron of strategy profiles that could possibly be made asymptotically stable under some reasonable deterministic dynamics. These faces are Kalai and Samet's (1984) persistent retracts and are spanned by Basu and Weibull's (1991) CURB sets based on a natural (and, in a well-defined sense, minimal) refinement of the best-reply correspondence. We show that such a correspondence satisfying basic properties such as existence, upper hemi-continuity, and convex-valuedness exists and is unique in most games. We introduce a notion of rationalizability based on this correspondence and its relation to other such concepts. We study its fixed-points and their relations to equilibrium refinements. We find, for instance, that a fixed point of the refined best reply correspondence in the agent normal form of any extensive form game constitutes a perfect Bayesian equilibrium, which is weak perfect Bayesian in every subgame. Finally, we study the index of its fixed point components.
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- Ritzberger, Klaus, 2002. "Foundations of Non-Cooperative Game Theory," OUP Catalogue, Oxford University Press, number 9780199247868, April.
- 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, 2009. "Leadership Games with Convex Strategy Sets," Discussion Paper Series dp525, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- 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.
- 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.
- 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.
- 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., 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.
- 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.
- Kets, Willemien & Voorneveld, Mark, 2005. "Learning to be prepared," SSE/EFI Working Paper Series in Economics and Finance 590, Stockholm School of Economics.
- Kets, W. & Voorneveld, M., 2005. "Learning to be Prepared," Discussion Paper 2005-117, Tilburg University, Center for Economic Research.
- Basu, Kaushik & Weibull, Jorgen W., 1991. "Strategy subsets closed under rational behavior," Economics Letters, Elsevier, vol. 36(2), pages 141-146, June.
- Basu, K. & Weibull, J., 1990. "Strategy Subsets Closed Under Rational Behavior," Papers 62, Princeton, Woodrow Wilson School - Discussion Paper.
- Basu, K. & Weibull, J.W., 1990. "Strategy Subsets Closed Under Rational Behaviour," Papers 479, Stockholm - International Economic Studies.
- 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.
- 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.
- Voorneveld, Mark, 2004. "Preparation," Games and Economic Behavior, Elsevier, vol. 48(2), pages 403-414, August.
- 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, 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.
- Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, July.
- 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. Full references (including those not matched with items on IDEAS)