An Epistemic Characterization of Extensive Form Rationalizability

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.

[1]  R. Aumann.  Backward induction and common knowledge of rationality , 1995 .

[2]  Robert Stalnaker,et al.  Belief revision in games: forward and backward induction 1 Thanks to the participants in the LOFT2 m , 1998 .

[3]  David M. Kreps,et al.  Rationality and knowledge in game theory , 1997 .

[4]  R. Myerson.  MULTISTAGE GAMES WITH COMMUNICATION , 1984 .

[5]  Richard C. Jeffrey,et al.  Knowledge, Belief, and Counterfactual Reasoning in Games , 1999 .

[6]  Robert J. Aumann,et al.  Reply to Binmore , 1996 .

[7]  G. Asheim,et al.  Admissibility and Common Knowledge , 1996 .

[8]  Marciano M. Siniscalchi,et al.  Hierarchies of Conditional Beliefs and Interactive Epistemology in Dynamic Games , 1999 .

[9]  P. Reny.  Backward Induction, Normal Form Perfection and Explicable Equilibria , 1992 .

[10]  Elchanan Ben-Porath,et al.  Rationality, Nash Equilibrium and Backwards Induction in Perfect-Information Games , 1997 .

[11]  Dov Samet,et al.  Hypothetical Knowledge and Games with Perfect Information , 1996 .

[12]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[13]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[14]  B. Bernheim.  Rationalizable Strategic Behavior , 1984 .

[15]  T. Tan,et al.  The Bayesian foundations of solution concepts of games , 1988 .

[16]  Eddie Dekel,et al.  Hierarchies of Beliefs and Common Knowledge , 1993 .

[17]  Pierpaolo Battigalli,et al.  Strategic Rationality Orderings and the Best Rationalization Principle , 1996 .

[18]  Pierpaolo Battigalli,et al.  On Rationalizability in Extensive Games , 1997 .

[19]  David M. Kreps,et al.  Signaling Games and Stable Equilibria , 1987 .

[20]  David Pearce.  Rationalizable Strategic Behavior and the Problem of Perfection , 1984 .

[21]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[22]  A. Rényi,et al.  On Conditional Probability Spaces Generated by a Dimensionally Ordered Set of Measures , 1956 .