The Complexity of Optimal Multidimensional Pricing

Xi Chen, Ilias Diakonikolas, Dimitris Paparas, Xiaorui Sun, Mihalis Yannakakis

Abstract: We resolve the complexity of revenue-optimal deterministic auctions in the unit-demand single-buyer Bayesian setting, i.e., the optimal item pricing problem, when the buyer's values for the items are independent. We show that the problem of computing a revenue-optimal pricing can be solved in polynomial time for distributions of support size 2 and its decision version is NP-complete for distributions of support size 3. We also show that the problem remains NP-complete for the case of identical distributions.