A Dynamic Level-k Model in Sequential Games

33 Pages Posted: 9 Aug 2012

See all articles by Teck Ho

Teck Ho

University of California, Berkeley - Haas School of Business

Xuanming Su

University of Pennsylvania - Operations & Information Management Department

Date Written: August 9, 2012

Abstract

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the "centipede game'', however, players frequently violate this principle. An alternative is a dynamic level-k model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level-k rule is a best-response to the level-(k-1) rule and the level-infinity rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Since the dynamic level-k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level-k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments.

Keywords: Level-k Models, Learning, Sequential Games, Backward Induction, Behavioral Game Theory

Suggested Citation

Ho, Teck and Su, Xuanming, A Dynamic Level-k Model in Sequential Games (August 9, 2012). Available at SSRN: https://ssrn.com/abstract=2127360 or http://dx.doi.org/10.2139/ssrn.2127360

Teck Ho

University of California, Berkeley - Haas School of Business ( email )

545 Student Services Building, #1900
2220 Piedmont Avenue
Berkeley, CA 94720
United States

Xuanming Su (Contact Author)

University of Pennsylvania - Operations & Information Management Department ( email )

Philadelphia, PA 19104
United States

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