A Statistical View of Learning in the Centipede Game

TL;DR

This paper investigates whether students learn the sub-game perfect equilibrium in the centipede game through repeated play, using statistical models that account for learning and within-player correlation, and compares different testing methods.

Contribution

It introduces a statistical model that captures learning dynamics and within-player correlation in the centipede game, improving upon previous models.

Findings

Model with learning fits data better than previous models.

Within-player correlation significantly affects decision outcomes.

Statistical tests vary in exploratory and confirmatory contexts.

Abstract

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.