Synthese 169 (2):301-333 (2009)

Authors
Sonja Smets
University of Amsterdam
Alexandru Baltag
University of Amsterdam
Jonathan Zvesper
University of Oxford
Abstract
We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we "simulate" the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning that the node is reached. We then use the notion of "stable belief, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann's and compatible with the implicit assumptions underlying Stalnaker's criticism of Aumann's proof. The "dynamic" nature of our concept of rationality explains why our condition avoids the apparent circularity of the "backward induction paradox": it is consistent to believe in a player's rationality after updating with his irrationality.
Keywords Philosophy   Metaphysics   Philosophy of Language   Logic   Epistemology   Computer Science, general   Philosophy of Science
Categories No categories specified
(categorize this paper)
DOI 10.1007/s11229-009-9559-z
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 58,374
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Two Modellings for Theory Change.Adam Grove - 1988 - Journal of Philosophical Logic 17 (2):157-170.
Logics of Public Communications.Jan Plaza - 2007 - Synthese 158 (2):165 - 179.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.

View all 15 references / Add more references

Citations of this work BETA

Logic in a Social Setting.Johan van Benthem - 2011 - Episteme 8 (3):227-247.

View all 8 citations / Add more citations

Similar books and articles

Doxastic Conditions for Backward Induction.Thorsten Clausing - 2003 - Theory and Decision 54 (4):315-336.
Backward-Induction Arguments: A Paradox Regained.Jordan Howard Sobel - 1993 - Philosophy of Science 60 (1):114-133.
Rationality and Backward Induction.Ken Binmore - 1997 - Journal of Economic Methodology 4 (1):23-41.
Backward Induction Without Common Knowledge.Cristina Bicchieri - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:329 - 343.
The Solution to the Surprise Exam Paradox.Ken Levy - 2009 - Southern Journal of Philosophy 47 (2):131-158.
Backward Induction and Rationality.K. G. Binmore & London School of Economics and Political Science - 1995 - London School of Economics, Centre for the Philosophy of the Natural and Social Sciences.
Agent Connectedness and Backward Induction.Christian W. Bach & Conrad Heilmann - 2011 - International Game Theory Review 13 (2):195-208.
Belief Revision in Games of Perfect Information.Thorsten Clausing - 2004 - Economics and Philosophy 20 (1):89-115.

Analytics

Added to PP index
2016-02-04

Total views
23 ( #456,489 of 2,420,544 )

Recent downloads (6 months)
1 ( #542,979 of 2,420,544 )

How can I increase my downloads?

Downloads

My notes