Substantive rationality and backward induction

Joseph Y. Halpern

pp. 923-932

in: Horacio Arló-Costa, Vincent F. Hendricks, Johan van Benthem (eds), Readings in formal epistemology, Berlin, Springer, 2016

Abstract

Aumann has proved that common knowledge of substantive rationality 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 difference between Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that lets us capture this difference, in which both Aumann's result and Stalnaker's result are true (under appropriate assumptions).