Monopoly pricing with optimal information

We analyze a monopoly pricing model where information about the buyer's valuation is endogenous. Before the seller sets a price, both the buyer and the seller receive private signals that may be informative about the buyer's valuation. The joint distribution of these signals, as a function of the valuation, is optimally chosen by the players. In general, players have conflicting incentives over the provision of information. As a modelling device, we assume that an aggregation function determines the information structure from the choices of the players, and we characterize the pure strategy equilibrium payoffs for a natural class of aggregation functions. Every equilibrium payoff can be achieved by an information structure that is the result of the seller trying to make both players uninformed while the buyer tries to learn about his valuation. Price discrimination is limited to the seller setting different prices for informed vs uninformed buyers.