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 (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), 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 (via public announcements) 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 (the “epistemic openness of the future”) 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 (continue to) believe in a player’s rationality after updating with his irrationality.
Keywords Backward induction  Dynamic logic  Epistemic logic  Public announcements  Rationality
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DOI 10.1007/s11229-009-9559-z
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References found in this work BETA

A Reply to My Critics.George Edward Moore - 1942 - In Paul Arthur Schilpp (ed.), The Philosophy of G. E. Moore. Open Court.
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.

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