  This paper presents an in-depth statistical analysis of an experiment
designed to measure the extent to which players in a simple game behave
according to a popular behavioral economic model. The p-beauty contest is a
multi-player number guessing game that has been widely used to study strategic
behavior. This paper describes beauty contest experiments for an audience of
data analysts, with a special focus on a class of models for game play called
k-step thinking models, which allow each player in the game to employ an
idiosyncratic strategy. We fit a Bayesian statistical model to estimate the
proportion of our player population whose game play is compatible with a k-step
thinking model. Our findings put this number at approximately 25%.
