Correlation-robust mechanism design

In this letter, we discuss the correlation-robust framework proposed by Carroll [Econometrica 2017] and our new development [SODA 2018]. Consider a monopolist seller that has n heterogeneous items to sell to a single buyer with the objective of maximizing the seller's revenue. In the correlation-robust framework, the seller only knows marginal distribution of each item but has no information about the 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 the given marginal distributions. Carroll's main result states that when the buyer's value for any set of her items is the sum of the values of individual items in the set, the optimal correlation-robust mechanism should sell items separately. We extend this result to the case where the buyer has a budget constraint on her total payment. Namely, we show that 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 per item budget constraint. We highlight an alternative approach via a dual Linear Programming formulation for the optimal correlation-robust mechanism design problem. This LP can be used to compute optimal mechanisms in general (other than additive) settings. It also yields an alternative proof for the additive monopoly problem without constructing the worst-case distribution and allows us to extend the proof to the budget setting.