Journal Article

A Dynamic Level-k Model in Sequential Games

Ho, Teck-Hua, Su, Xuanming

2013

Overview

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- ∞ 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. Because 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. This paper was accepted by Peter Wakker, decision analysis.

• Publisher: INFORMS,Institute for Operations Research and the Management Sciences
• Subject: Alternative approaches / Analysis / Backward induction / Bargaining / Behavior / behavioral game theory / Cognitive models / Dynamic modeling / Dynamic programming / Economic behaviour / Economic models / Economic theory / Expected utility / Experimental economics / Experimental methods / Experiments / Game theory / Games / Generalizability / Hierarchies / Induction / Learning / level / Management science / Methods / Modeling / Organizational behavior / Property rights / Repetition / Rules / Sequential analysis / Sequential game / sequential games / Spieltheorie / Studies / Theoretical econometrics / Verhalten / Violations