The $p$-beauty contest is a multi-player number guessing game that is widely used to study strategic behavior. Using new data from a specially-designed web experiment, we examine the evidence in favor of a popular class of behavioral economic models called $k$-step thinking models. After fitting a custom Bayesian spline model to the experimental data, we estimate that the proportion of players who could be using a $k$-step thinking strategy is approximately 25%.
"A Bayesian hierarchical model for inferring player strategy types in a number guessing game." Ann. Appl. Stat. 9 (3) 1459 - 1483, September 2015. https://doi.org/10.1214/15-AOAS830