Substantive Rationality and Backward Induction

Aumann has proved that common knowledge of substantive ratio-nality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking , a player is substantively rational if, for all vertices v, if the player were to reach vertex v, then the player would be rational at vertex v". It is shown here that the key diierence between Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that lets us capture this diierence, in which both Aumann's result and Stalnaker's result are true (under appropriate assumptions). there has been intense scrutiny of the assumption of common knowledge of rationality, the use of counterfactual reasoning in games, and the role of common knowledge and counterfactuals in the arguments for backward