A Bayesian hierarchical model for inferring player strategy types in a number guessing game

TL;DR

This paper develops a Bayesian hierarchical model to analyze player strategies in a number guessing game, estimating that about 25% of players follow a k-step thinking behavioral model.

Contribution

It introduces a Bayesian hierarchical approach to infer the prevalence of k-step thinking strategies among players in a behavioral game experiment.

Findings

Approximately 25% of players exhibit k-step thinking behavior.

The model effectively distinguishes strategy types in the game.

The approach provides a quantitative measure of strategic complexity.

Abstract

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%.