Bayesian Learning in Markets with Common Value

Abstract: Consider a Bertrand competition between firms which produce substitute goods on the one hand and many consumers with a common value on the other hand. Assume consumers receive some private signals regarding the identity of the superior product, inducing a demand uncertainty. Will such markets aggregate information? Will the superior firm necessary prevail? We study these questions in two scenarios – one in which consumers buy simultaneously and hence can not respond to each other’s actions and another where buying is done sequentially. We provide necessary and sufficient conditions on the fundamentals of the problem – the prior probabilities and signal distribution – to guarantee information aggregation and learning. We introduce a novel property over the signals, referred to as Vanishing Likelihood, which is necessary for social learning. Our results contribute to the literature of monopolistic entry deterrence on the one hand and herding on the other.