Markov Chain Monte Carlo for Incomplete Information Discrete Games

This paper outlines a Bayesian approach to estimating discrete games of incomplete information. The MCMC routine proposed features two changes to the traditional Metropolis-Hastings algorithm to facilitate the estimation of games. First, we propose a new approach to sample equilibrium probabilities using a probabilistic equilibrium selection rule that allows for the evaluation of the parameter posterior. Second, we propose a di¤erential evolution based MCMC sampler which is capable of handling the unwieldy posterior that only has support on the equilibrium manifold. We also present two applications to demonstrate the feasibility of our proposed methodology.