Substantive Rationality and Backward Induction
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).Download Info
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Paper provided by EconWPA in its series Game Theory and Information with number 0004008.Length: 12 pages
Date of creation: 22 Nov 2000
Date of revision:
Handle: RePEc:wpa:wuwpga:0004008
Note: Type of Document - PDF; prepared on Unix; pages: 12; figures: included. To appear, Games and Economic Behavior.
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Web page: http://128.118.178.162
Related research
Keywords: Substantive rationality; backward induction; games of perfect information; counterfactuals;Other versions of this item:
- Halpern, Joseph Y., 2001. "Substantive Rationality and Backward Induction," Games and Economic Behavior, Elsevier, vol. 37(2), pages 425-435, November.
- C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
- C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2001-02-14 (All new papers)
References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stalnaker, Robert, 1996. "Knowledge, Belief and Counterfactual Reasoning in Games," Economics and Philosophy, Cambridge University Press, vol. 12(02), pages 133-163, October.
- Stalnaker, Robert, 1998. "Belief revision in games: forward and backward induction1," Mathematical Social Sciences, Elsevier, vol. 36(1), pages 31-56, July.
- Samet, Dov, 1996.
"Hypothetical Knowledge and Games with Perfect Information,"
Games and Economic Behavior,
Elsevier, vol. 17(2), pages 230-251, December.
- Dov Samet, 1994. "Hypothetical Knowledge and Games with Perfect Information," Game Theory and Information 9408001, EconWPA, revised 17 Aug 1994.
- Philip J. Reny, 1992. "Rationality in Extensive-Form Games," Journal of Economic Perspectives, American Economic Association, vol. 6(4), pages 103-118, Fall.
- Binmore, Ken, 1987. "Modeling Rational Players: Part I," Economics and Philosophy, Cambridge University Press, vol. 3(02), pages 179-214, October.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Giacomo Bonanno, 2011.
"Reasoning about strategies and rational play in dynamic games,"
Working Papers
1111, University of California, Davis, Department of Economics.
- Bonanno, Giacomo, 2011. "Reasoning about Strategies and Rational Play in Dynamic Games," Working Papers 11-11, University of California at Davis, Department of Economics.
- Bonanno, Giacomo, 2012.
"A Dynamic Epistemic Characterization of Backward Induction without Counterfactuals,"
Working Papers
12-02, University of California at Davis, Department of Economics.
- Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
- Giacomo Bonanno, 2012. "A dynamic epistemic characterization of backward induction without counterfactuals," Working Papers 122, University of California, Davis, Department of Economics.
- Bonanno, Giacomo, 2003. "A syntactic characterization of perfect recall in extensive games," Research in Economics, Elsevier, vol. 57(3), pages 201-217, September.
- Giacomo Bonanno, 2008.
"Non-cooperative game theory,"
Working Papers
86, University of California, Davis, Department of Economics.
- Bonanno, Giacomo, 2008. "Non-cooperative Game Theory," Working Papers 08-6, University of California at Davis, Department of Economics.
- Bonanno, Giacomo, 2012. "Epistemic Foundations of Game Theory," Working Papers 2012-11, University of California at Davis, Department of Economics.
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