Non-neutral information costs with match-value uncertainty

This paper investigates a model featuring a monopolist seller and a buyer with an uncertain valuation for the seller’s product. The seller chooses an information system which allows the buyer to receive a private signal, potentially correlated with her valuation. No restrictions are imposed on the conditional distributions of the signal; the cost of the information system is proportional to its precision, measured by the mutual information between the distributions of the buyer’s valuation and the signal. In equilibrium, the information system trades off the information cost against the losses deriving from a probability of trade that is either “too high,” or “too low”—depending on the relative weight of the expected losses resulting from errors of the two types—and sends “non-neutral” signals, typically. Thus, in general, the probability of a correct signal depends on the buyer’s actual valuation, and the probability of trade differs from the probability of a valuation exceeding the cost of production. The expected total surplus generated by the exchange is maximized, in equilibrium.