Finite mixture analysis of beauty-contest data using generalised beta distributions

Abstract

This paper introduces a mixture model based on the beta distribution, without preestablished means and variances, to analyze a large set of Beauty-Contest data obtained from diverse groups of experiments (Bosch-Domenech et al. 2002). This model gives a better t of the experimental data, and more precision to the hypothesis that a large proportion of individuals follow a common pattern of reasoning, described as iterated best reply (degenerate), than mixture models based on the normal distribution. The analysis shows that the means of the distributions across the groups of experiments are pretty stable, while the proportions of choices at dierent levels of reasoning vary across groups.Keywords: Beauty-Contest experiments, decision theory, reasoning hierarchy, finite mixture distribution, beta distribution, EM algorithm.