Bayesian learning in markets with common value

Two firms produce substitute goods with unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the firms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the superior firm necessarily prevail? We adapt the classical social learning model by introducing strategic dynamic pricing. We provide necessary and sufficient conditions for learning. In contrast to previous results, learning can occur when signals are bounded. This happens when signals exhibit the newly introduced vanishing likelihood property.