Substantive Rationality and Backward Induction
AbstractAumann 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 InfoPaper 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:
Note: Type of Document - PDF; prepared on Unix; pages: 12; figures: included. To appear, Games and Economic Behavior.
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Substantive rationality; backward induction; games of perfect information; counterfactuals;
Other versions of this item:
- 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)
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