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 prices paid for purchasing an item or not. 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 pair of prices is optimal for the seller. The optimal mechanism is a subsidized posted price that provides a 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 analyze non-linear pricing contracts.