Open Access
2008 Common Knowledge of Rationality in Extensive Games
Boudewijn de Bruin
Notre Dame J. Formal Logic 49(3): 261-280 (2008). DOI: 10.1215/00294527-2008-011


We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with a principle of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility


Download Citation

Boudewijn de Bruin. "Common Knowledge of Rationality in Extensive Games." Notre Dame J. Formal Logic 49 (3) 261 - 280, 2008.


Published: 2008
First available in Project Euclid: 15 July 2008

zbMATH: 1154.91009
MathSciNet: MR2428554
Digital Object Identifier: 10.1215/00294527-2008-011

Primary: 03B42 , 91A18 , 91A26

Keywords: common knowledge , epistemic characterization theorem , rationality

Rights: Copyright © 2008 University of Notre Dame

Vol.49 • No. 3 • 2008
Back to Top