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.
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- Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
- Bernheim, B Douglas, 1984.
"Rationalizable Strategic Behavior,"
Econometric Society, vol. 52(4), pages 1007-28, July.
- Battigalli, Pierpaolo, 1996. "Strategic Rationality Orderings and the Best Rationalization Principle," Games and Economic Behavior, Elsevier, vol. 13(2), pages 178-200, April.
- Dov Samet, 1994.
"Hypothetical Knowledge and Games with Perfect Information,"
Game Theory and Information
9408001, EconWPA, revised 17 Aug 1994.
- Samet, Dov, 1996. "Hypothetical Knowledge and Games with Perfect Information," Games and Economic Behavior, Elsevier, vol. 17(2), pages 230-251, December.
- Martin J Osborne & Ariel Rubinstein, 2009.
"A Course in Game Theory,"
814577000000000225, UCLA Department of Economics.
- Myerson, Roger B, 1986.
"Multistage Games with Communication,"
Econometric Society, vol. 54(2), pages 323-58, March.
- 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.
- Pierpaolo Battigalli, . "Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games," Working Papers 111, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- Adam Brandenburger & Eddie Dekel, 2014.
"Hierarchies of Beliefs and Common Knowledge,"
World Scientific Book Chapters,
in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41
World Scientific Publishing Co. Pte. Ltd..
- 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, March.
- Aumann, Robert J., 1996. "Reply to Binmore," Games and Economic Behavior, Elsevier, vol. 17(1), pages 138-146, November.
- 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.
- Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
- 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.
- Reny, Philip J, 1992. "Backward Induction, Normal Form Perfection and Explicable Equilibria," Econometrica, Econometric Society, vol. 60(3), pages 627-49, May.
- Aumann, Robert J., 1995. "Backward induction and common knowledge of rationality," Games and Economic Behavior, Elsevier, vol. 8(1), pages 6-19.
- 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.
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