Refinements of rationalizability for normal-form games
AbstractIn normal-form games, rationalizability (Bernheim , Pearce ) on its own fails to exclude some very implausible strategy choices. Three main refinements of rationalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate unreasonable outcomes and suffer from several drawbacks. Therefore, we introduce the trembling-hand rationalizability concept, where the players' actions have to be best responses also against perturbed conjectures. We also propose another refinement: weakly perfect rationalizability, where players' actions that are not best responses are only played with a very small probability. We show the relationship between perfect rationalizability and weakly perfect rationalizability as well as the relationship between proper rationalizability and weakly perfect rationalizability : weakly perfect rationalizability is a weaker refinement than both perfect and proper rationalizability. Moreover, in two-player games it holds that weakly perfect rationalizability is a weaker refinement than trembling-hand rationalizability. The other relationships between the various refinements are illustrated by means of examples. For the relationship between any other two refinements we give examples showing that the remaining set of strategies corresponding to the first redinement can be either smaller or larger than the one corresponding to the second refinement.
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Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers RP with number -1378.
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Note: In : International Journal of Game Theory, 28, 53-68, 1999
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Other versions of this item:
- Vincent J. Vannetelbosch & P. Jean-Jacques Herings, 1999. "Refinements of rationalizability for normal-form games," International Journal of Game Theory, Springer, vol. 28(1), pages 53-68.
- Herings, P.J.J. & Vannetelbosch, V., 1997. "Refinements of Rationalizability for Normal-Form Games," Discussion Paper 1997-03, Tilburg University, Center for Economic Research.
- HERINGS, Jean - Jacques & VANNETELBOSCH, Vincent, 1997. "Refinements of rationalizability for normal-form games," CORE Discussion Papers 1997002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
514, David K. Levine.
- Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
- Vannetelbosch, Vincent J., 1996. "Refinements of Rationalizability for Normal-Form Games: The Main Ideas," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- Kohlberg, Elon & Mertens, Jean-Francois, 1986.
"On the Strategic Stability of Equilibria,"
Econometric Society, vol. 54(5), pages 1003-37, September.
- E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, 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).
- van Damme, Eric, 1989.
"Stable equilibria and forward induction,"
Journal of Economic Theory,
Elsevier, vol. 48(2), pages 476-496, August.
- Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
- Damme, E.E.C. van, 1989. "Stable equilibria and forward induction," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154422, Tilburg University.
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