Advertisement

Substantive Rationality and Backward Induction

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

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).

Keywords

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.

Notes

Acknowledgements

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

References

  1. Aumann, R. J. (1976). Agreeing to disagree. Annals of Statistics, 4(6), 1236–1239.CrossRefGoogle Scholar
  2. Aumann, R. J. (1995). Backwards induction and common knowledge of rationality. Games and Economic Behavior, 8, 6–19.CrossRefGoogle Scholar
  3. Bicchieri, C. (1988). Strategic behavior and counterfactuals. Synthese, 76, 135–169.CrossRefGoogle Scholar
  4. Bicchieri, C. (1989). Self refuting theories of strategic interaction: A paradox of common knowledge. Erkenntnis, 30, 69–85.CrossRefGoogle Scholar
  5. Binmore, K. (1987). Modeling rational players I. Economics and Philosophy, 3, 179–214. Part II appeared ibid., 4, 9–55.Google Scholar
  6. Halpern, J. Y. (1999). Hypothetical knowledge and counterfactual reasoning. International Journal of Game Theory, 28(3), 315–330.CrossRefGoogle Scholar
  7. Reny, P. (1992). Rationality in extensive form games. Journal of Economic Perspectives, 6, 103–118.CrossRefGoogle Scholar
  8. Samet, D. (1996). Hypothetical knowledge and games with perfect information. Games and Economic Behavior, 17, 230–251.CrossRefGoogle Scholar
  9. Selten, R. (1975). Reexamination of the perfectness concept for equilibrium points in extensive games. International Journal of Game Theory, 4, 25–55.CrossRefGoogle Scholar
  10. Stalnaker, R. (1998). Belief revision in games: Forward and backward induction. Mathematical Social Sciences, 36, 31–56.CrossRefGoogle Scholar
  11. Stalnaker, R. C. (1996). Knowledge, belief and counterfactual reasoning in games. Economics and Philosophy, 12, 133–163.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Computer Science DepartmentCornell UniversityIthacaUSA

Personalised recommendations