Substantive Rationality and Backward Induction

  • Joseph Y. HalpernEmail author
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)


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).


Selection Function Common Knowledge Perfect Information Strategy Profile Game Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I’d like to thank Robert Stalnaker for his many useful comments and criticisms of this paper.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA

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