Modeling of the learning process in centipede games

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

[1]  A. Westveld,et al.  A Statistical View of Learning in the Centipede Game , 2010, 1003.2253.

[2]  K. Binmore Rationality and Backward Induction , 1997 .

[3]  Peter J. Diggle,et al.  Simple Monte Carlo Tests for Spatial Pattern , 1977 .

[4]  R. McKelvey,et al.  An experimental study of the centipede game , 1992 .

[5]  R. McKelvey,et al.  Quantal Response Equilibria for Extensive Form Games , 1998 .

[6]  R. McKelvey,et al.  A STATISTICAL THEORY OF EQUILIBRIUM IN GAMES , 1996 .

[7]  R. McKelvey,et al.  Quantal Response Equilibria for Normal Form Games , 1995 .

[8]  S. L. Andersen,et al.  Permutation Theory in the Derivation of Robust Criteria and the Study of Departures from Assumption , 1955 .

[9]  L. Samuelson Economic Theory and Experimental Economics , 2005 .

[10]  Robert Stalnaker Knowledge, Belief and Counterfactual Reasoning in Games , 1996, Economics and Philosophy.

[11]  Philip A. Haile,et al.  On the Empirical Content of Quantal Response Equilibrium , 2003 .

[12]  Curtis S. Signorino Strategic Interaction and the Statistical Analysis of International Conflict , 1999, American Political Science Review.

[13]  Gareth O. Roberts,et al.  Examples of Adaptive MCMC , 2009 .

[14]  Thomas R. Palfrey,et al.  A Bayesian Sequential Experimental Study of Learning in Games , 1993 .

[15]  D. McFadden Conditional logit analysis of qualitative choice behavior , 1972 .

[16]  R. Aumann Backward induction and common knowledge of rationality , 1995 .