The Annals of Applied Statistics

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

P. Richard Hahn, Indranil Goswami, and Carl F. Mela

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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%.

Article information

Ann. Appl. Stat. Volume 9, Number 3 (2015), 1459-1483.

Received: September 2014
Revised: April 2015
First available in Project Euclid: 2 November 2015

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Zentralblatt MATH identifier

Behavioral game theory hierarchical modeling partial identification


Hahn, P. Richard; Goswami, Indranil; Mela, Carl F. A Bayesian hierarchical model for inferring player strategy types in a number guessing game. Ann. Appl. Stat. 9 (2015), no. 3, 1459--1483. doi:10.1214/15-AOAS830.

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Supplemental materials

  • Supplement to “A Bayesian hierarchical model for inferring player strategy types in a number guessing game”. The supplement contains computational details and a sensitivity analysis based on model residuals.