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A Statistical View of Learning in the Centipede Game

In this article we evaluate the statistical evidence that a population of students learn about the subgame perfect Nash equilibrium of the centipede game via repeated play of the game. This is done by formulating a model in which a player's error in assessing the utility of game decisions changes as they gain experience with the game. We first estimate parameters in a statistical model where the probabilities of choices of the players are given by a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey (1995, 1996, 1998)), but are allowed to change with repeated play. This model gives a better fit to the data than similar models previously considered. However, substantial correlation of outcomes of games having a common player suggests that a statistical model that captures within-subject correlation is more appropriate. We estimate parameters in a model which allows for within-player correlation of decisions, and population-specific rates of learning.

Key words: Game Theory, Centipede Game, Learning, Quantal Response Equilibrium, Bayesian Statistics, Random Effects Modelling, Hierarchical Modelling, Monte Carlo p-values, Dyadic data