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Revealed Preference Implications of Backward Induction and Subgame Perfection†

Revealed Preference Implications of Backward Induction and Subgame Perfection† AbstractConsider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Economic Journal: Microeconomics American Economic Association

Revealed Preference Implications of Backward Induction and Subgame Perfection†

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Publisher
American Economic Association
Copyright
Copyright © 2020 © American Economic Association
ISSN
1945-7685
DOI
10.1257/mic.20180077
Publisher site
See Article on Publisher Site

Abstract

AbstractConsider a decision-maker (DM) who must select an alternative from a set of mutually exclusive alternatives but must take this decision sequentially. If the DM’s choice correspondence over subsets of alternatives satisfies the weak axiom of revealed preference (WARP), then the subgame perfect Nash equilibrium (SPNE) and backward induction (BI) strategies coincide. We study the relation between the SPNE and BI strategies when the DM’s choice correspondence fails to satisfy WARP. First, Sen’s axiom α is necessary and sufficient for the set of SPNE strategies to be a subset of the set of BI strategies; moreover, a mild strengthening of Sen’s axiom β is necessary and sufficient for the set of BI strategies to be a subset of the set of SPNE strategies. These results extend to multiplayer games. (JEL D11, C72, C73)

Journal

American Economic Journal: MicroeconomicsAmerican Economic Association

Published: May 1, 2020

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