An Epistemic Characterisation of Extensive Form Rationalisability
We use an extensive form, universal type space to provide the following epistemic characterisation of extensive form rationalisability. Say that player i strongly believes event E if i is certain of E conditional on each of her information sets consistent with E. Our main contribution is to show that a strategy profile s is extensive form rationalisable if and only if there is a state in which s is played and (0) everybody is rational, (1) everybody strongly believes (0), (2) everybody strongly believes (0) & (1), (3) everybody strongly believes (0) & (1) & (2), .... This result also allows us to provide sufficient epistemic conditions for the backward induction outcome and to relate extensive form rationalisability and conditional common certainty of rationality.
|Date of creation:||Feb 1999|
|Date of revision:|
|Contact details of provider:|| Postal: Corso Magenta, 63 - 20123 Milan|
Web page: http://www.feem.it/
More information through EDIRC
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.:
- In-Koo Cho & David M. Kreps, 1987.
"Signaling Games and Stable Equilibria,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 102(2), pages 179-221.
- Pierpaolo Battigalli, .
"Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games,"
111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Battigalli, Pierpaolo & Siniscalchi, Marciano, 1999. "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Journal of Economic Theory, Elsevier, vol. 88(1), pages 188-230, September.
- Roger B. Myerson, 1984.
"Multistage Games with Communication,"
590, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Samet, Dov, 1996.
"Hypothetical Knowledge and Games with Perfect Information,"
Games and Economic Behavior,
Elsevier, vol. 17(2), pages 230-251, December.
- Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
- Elchanan Ben-Porath, 1997. "Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games," Review of Economic Studies, Oxford University Press, vol. 64(1), pages 23-46.
- Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
- Battigalli, Pierpaolo, 1997. "On Rationalizability in Extensive Games," Journal of Economic Theory, Elsevier, vol. 74(1), pages 40-61, May.
- Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
- Brandenburger Adam & Dekel Eddie, 1993.
"Hierarchies of Beliefs and Common Knowledge,"
Journal of Economic Theory,
Elsevier, vol. 59(1), pages 189-198, February.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
- Ronald Fagin & Joseph Y. Halpern & Yoram Moses & Moshe Y. Vardi, 2003. "Reasoning About Knowledge," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262562006.
- Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
- Martin J Osborne & Ariel Rubinstein, 2009.
"A Course in Game Theory,"
814577000000000225, UCLA Department of Economics.
- D. B. Bernheim, 2010.
"Rationalizable Strategic Behavior,"
Levine's Working Paper Archive
514, David K. Levine.
- Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
- Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
When requesting a correction, please mention this item's handle: RePEc:fem:femwpa:1999.25. 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: (barbara racah)
If references are entirely missing, you can add them using this form.