  In this article we evaluate the statistical evidence that a population of
students learn about the sub-game 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 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. Thus we then estimate
parameters in a model which allows for within-player correlation of decisions
and rates of learning. Through out the paper we also consider and compare the
use of randomization tests and posterior predictive tests in the context of
exploratory and confirmatory data analyses.
