Separation in Correlation-Robust Monopolist Problem with Budget

Abstract

We consider a monopolist seller that has n heterogeneous items to sell to a single buyer. The seller's goal is to maximize her revenue. We study this problem in the correlation-robust framework recently proposed by Carroll [Econometrica 2017]. In this framework, the seller only knows marginal distributions for each separate item but has no information about correlation across different items in the joint distribution. Any mechanism is then evaluated according to its expected profit in the worst-case, over all possible joint distributions with given marginal distributions. Carroll's main result states that in multi-item monopoly problem with buyer, whose value for a set of items is additive, the optimal correlation-robust mechanism should sell items separately. We use alternative dual Linear Programming formulation for the optimal correlation-robust mechanism design problem. This LP can be used to compute optimal mechanisms in general settings. We give an alternative proof for the additive monopoly problem without constructing worst-case distribution. As a surprising byproduct of our approach we get that separation result continues to hold even when buyer has a budget constraint on her total payment. Namely, the optimal robust mechanism splits the total budget in a fixed way across different items independent of the bids, and then sells each item separately with a respective per item budget constraint.

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