Econometrics and Applied Micro Seminar

This paper addresses a basic question in the field of behavioral game theory using Bayesian hierarchical modeling applied to data from a new p-beauty contest web experiment. Specifically, we assess whether subjects apply k-step reasoning as is routinely assumed in previous literature. Collecting experimental p-beauty contest data across multiple values of p per subject, we estimate a nonlinear random effects regression model to infer an upper bound on the probability that a randomly selected subject will play a strategy compatible with k-step reasoning. While some individuals appear to adopt strategies compatible with k-step reasoning, the proportion of individuals who do so appears to be less than 30%.

Our new statistical model overcomes two inferential hurdles. First, a fundamental identification problem lies at the heart of behavioral game theory data: we never observe strategic thinking itself, only its game-play manifestations. We take a partial-identification approach, estimating an upper bound on the quantity we ultimately would wish to learn (the proportion of k-step thinkers in the player population). Second, estimating this proportion amounts to judging which inferred regression curves are increasing convex functions; structuring a hierarchical model appropriate to this task requires special care to avoid overshrinking which we handle by introducing a robust hierarchical prior.