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 ra- tionalizability have been proposed in the literature: cautious, perfect, and proper rationalizability. Nevertheless, some of these refinements also fail to eliminate un- reasonable 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 ratio- nalizability 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 rational- izability. 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 re- finement can be either smaller or larger than the one corresponding to the second refinement.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1997002.
Date of creation: 01 Jan 1997
Date of revision:
Contact details of provider:
Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
Fax: +32 10474304
Web page: http://www.uclouvain.be/core
More information through EDIRC
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, P. Jean-Jacques & ANNETELBOSCH, Vincent J., . "Refinements of rationalizability for normal-form games," CORE Discussion Papers RP -1378, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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.:
- 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.
- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
661465000000000381, David K. Levine.
- van Damme,Eric, 1987.
"Stable equilibria and forward induction,"
Discussion Paper Serie A
128, University of Bonn, Germany.
- Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
- Borgers, Tilman & Samuelson, Larry, 1992. ""Cautious" Utility Maximization and Iterated Weak Dominance," International Journal of Game Theory, Springer, vol. 21(1), pages 13-25.
- 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).
- 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).
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral 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: (Alain GILLIS).
If references are entirely missing, you can add them using this form.