Modeling of the learning process in centipede games

• Published in: Stat (International Statistical Institute) Vol. 2; no. 1; pp. 242 - 254
• Main Authors: Westveld, Anton H., Hoff, Peter D.
• Format: Journal Article
• Language: English
• Published: The Hague Blackwell Publishing Ltd 01-12-2013; Wiley Subscription Services, Inc
• Subjects: Bayesian inference; game theory; hierarchical modeling; interaction/relational data; quantal response equilibrium
• ISSN: 2049-1573; 2049-1573
• DOI: 10.1002/sta4.32

According to classic game theory, individuals playing a centipede game learn about the subgame perfect Nash equilibrium via repeated play of the game. We employ statistical modeling to evaluate the evidence of such learning processes while accounting for the substantial within‐player correlation observed for the players’ decisions and rates of learning. We determine the probabilities of players’ choices through a quantal response equilibrium. Our statistical approach additionally (i) relaxes the assumption of players’ a priori global knowledge of opponents’ strategies, (ii) incorporates within‐subject dependency through random effects, and (iii) allows players’ decision probabilities to change with repeated play through an explicit covariate. Hence, players’ tendencies to correctly assess the utility of decisions are allowed to evolve over the course of the game, and both adaptive behavior as one accrues experience and the difference in this behavior between players are appropriately reflected by the model. Copyright © 2013 John Wiley & Sons Ltd