Substantive rationality and backward induction

Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. StaInaker has proved that it does not, Roughly speaking, a player is substantively ra tional if for all vertices v, if the player were to reach vertex v, then he would be rational at vertex v. It is shown here that the key difference be tween Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that captures this difference, in which both Au mann's result and Stalnaker's result are true (under appropriate assumption s). (C) 2001 Academic Press.