We present a continuous-time model of Bayesian learning in a duopolistic market. Initially the value of one product offered is unknown to the market. The market participants learn more about the true value of the product as experimentation occurs over time. Firms set prices to induce experimentation with their product. The aggregate outcomes are public information.
As agents learn from the experiments of others, informational externalities arise. Surprisingly, the informational externality leads to too much learning. Buyers do not consider the impact of their experimentation on other buyers while the sellers internalize the gains from experiments conducted by the buyers. The firms free ride on the market as the social costs of experiments are not appropriately reflected in the equilibrium prices. The value functions of the sellers display preference for information in contrast to the buyers who are information averse.
We determine Markov Perfect Equilibrium prices and allocations in this two-sided learning model. The analysis is presented for a finite number of buyers as well as for a continuum of buyers. The severity of the inefficiency is shown to be monotonically increasing in the number of buyers.