Optimal discriminatory disclosure

A seller of an indivisible good designs a selling mechanism for a buyer whose private information (his type) is the distribution of his value for the good. A selling mechanism includes both a menu of sequential pricing, and a menu of information disclosure about the realized value that the buyer is allowed to learn privately. In a model of two types with an increasing likelihood ratio, we show that under some regularity conditions the disclosure policy in an optimal mechanism has a nested interval structure: the high type is allowed to learn whether his value is greater than the seller's cost, while the low type is allowed to learn whether his value is in an interval above the cost. The interval of the low type may exclude values at the top of the distribution to reduce the information rent of the high type. Information discrimination is in general necessary in an optimal mechanism.