Separation in Distributionally Robust Monopolist Problem

We consider a monopoly pricing problem, where a seller has multiple items to sell to a single buyer, only knowing the distribution of the buyer’s value profile. The seller’s goal is to maximize her expected revenue. In general, this is a difficult problem to solve, even if the distribution is well specified. In this paper, we solve a subclass of this problem when the distribution is assumed to belong to the class of distributions defined by given marginal partial information. Under this model, we show that the optimal strategy for the seller is a randomized posted price mechanism under which the items are sold separately, and the result continues to hold even when the buyer has a budget feasibility constraint. Consequently, under some specific ambiguity sets which include moment-based and Wasserstein ambiguity sets, we provide analytical solutions for these single-item problems. Based on the additive separation property, we show the general additive separation problem is a special case of resource allocation problems that can be solved by known polynomial-time algorithms.