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The Bounds of ReasonGame Theory and the Unification of the Behavioral Sciences$
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Herbert Gintis

Print publication date: 2014

Print ISBN-13: 9780691160849

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691160849.001.0001

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Extensive Form Rationalizability

Extensive Form Rationalizability

Chapter:
(p.106) 5 Extensive Form Rationalizability
Source:
The Bounds of Reason
Author(s):

Herbert Gintis

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691160849.003.0005

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible). Backward induction, by far the most popular technique, employs the iterated elimination of weakly dominated strategies, arriving at the subgame perfect Nash equilibria—the equilibria that remain Nash equilibria in all subgames. An extensive form game is considered generic if it has a unique subgame perfect Nash equilibrium. This chapter develops the tools of modal logic and presents Robert Aumann's famous proof that common knowledge of rationality (CKR) implies backward induction. It concludes that Aumann is perfectly correct, and the real culprit is CKR itself. CKR is in fact self-contradictory when applied to extensive form games.

Keywords:   common knowledge of rationality, CKR, extensive form games, game theory, backward induction, forward induction, Robert Aumann

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