Analyzing Ultimatum Bargaining: A Bayesian Approach to the Comparison of Two Potency Curves Under Shape Constraints

Abstract

An experiment designed to test whether experimenter observation influences play of the ultimatum game led to a comparison of proportions of perfect equilibria obtained under different conditions. Our analysis features a Bayesian approach to this comparison. Our method extends recent work in the nonparametric Bayesian analysis of bioassay problems when the prior constrains the form of the potency curve. Sampling-based approaches to calculating posterior features of interest are used and discussed. We conclude that experimenter observation has a small influence but not enough to account for most of the deviation from perfect-equilibrium play.

KEY WORDS:

• Dirichlet prior
• Gibbs sampling
• Importance resampling
• Perfect equilibrium
• Ultimatum game