A two-dimensional problem of revenue maximization

We consider the problem of finding the mechanism that maximizes the revenue of a seller of multiple objects. This problem turns out to be significantlymore complex than the casewhere there is only a single object (which was solved by Myerson, 1981). The analysis is difficult even in the simplest case studied here, where there are two exclusive objects and a single buyer, with valuations uniformly distributed on triangular domains. We show that the optimal mechanisms are piecewise linear with either 2 or 3 pieces, and obtain explicit formulas for most cases of interest. © 2011 Elsevier B.V. All rights reserved.