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Substantive Rationality and Backward Induction

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  • Halpern, Joseph Y.

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).

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 37 (2001)
Issue (Month): 2 (November)
Pages: 425-435

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Handle: RePEc:eee:gamebe:v:37:y:2001:i:2:p:425-435

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
  2. Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
  3. Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
  4. Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
  5. Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
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Cited by:
  1. Bonanno, Giacomo, 2003. "A syntactic characterization of perfect recall in extensive games," Research in Economics, Elsevier, vol. 57(3), pages 201-217, September.
  2. Christian W. Bach & Conrad Heilmann, 2009. "Agent connectedness and backward induction," LSE Research Online Documents on Economics 27000, London School of Economics and Political Science, LSE Library.
  3. Giacomo Bonanno, 2008. "Non-cooperative game theory," Working Papers 86, University of California, Davis, Department of Economics.
  4. Giacomo Bonanno, 2014. "Reasoning about strategies and rational play in dynamic games," Working Papers 149, University of California, Davis, Department of Economics.
  5. Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
  6. Giacomo Bonanno, 2013. "Counterfactuals and the Prisoner’s Dilemma," Working Papers 137, University of California, Davis, Department of Economics.

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