Optimal Mechanisms for a Value Maximizer : The Futility of Screening Targets

Motivated by the increased adoption of autobidding algorithms in internet advertising markets, we study the design of optimal mechanisms for selling items to a value-maximizing buyer with a return-on-spend constraint. The buyer's values and target ratio in the return-on-spend constraint are private. We restrict attention to deterministic sequential screening mechanisms that can be implemented as a menu of two-part tariffs. The main result of this paper is to provide a characterization of an optimal mechanism. Surprisingly, we show that the optimal mechanism does not require target screening, i.e., offering a single two-part tariff is optimal for the seller. The optimal mechanism is a subsidized two-part tariff that provides a lump-sum subsidy to the buyer to encourage participation and then charges a fixed unit price for each item sold. The seller's problem is a challenging non-linear mechanism design problem, and a key technical contribution of our work is to provide a novel approach to analyzing non-linear pricing contracts for constrained buyers. Our results have valuable implications for advertising platforms seeking to personalize pricing decisions based on advertisers' characteristics