We study the classic sequential screening problem under ex-post participation constraints. Thus the seller is required to satisfy buyers’ ex-post participation constraints. A leading example is the online display advertising market, in which publishers frequently cannot use up-front fees and instead use transaction-contingent fees. We establish when the optimal selling mechanism is static (buyers are not screened) or dynamic (buyers are screened), and obtain a full characterization of such contracts. We begin by analyzing our model within the leading case of exponential distributions with two types. We provide a necessary and suﬀicient condition for the optimality of the static contract. If the means of the two types are suﬀiciently close, then no screening is optimal. If they are suﬀiciently apart, then a dynamic contract becomes optimal. Importantly, the latter contract randomizes the low type buyer while giving a deterministic allocation to the high type. It also makes the low type worse-oﬀ and the high type better-oﬀ compared to the contract the seller would oﬀer if he knew the buyer’s type. Our main result establishes a necessary and suﬀicient condition under which the static contract is optimal for general distributions. We show that when this condition fails, a dynamic contract that randomizes the low type buyer is optimal.
Bergemann, Dirk; Castro, Francisco; and Weintraub, Gabriel, "The Scope of Sequential Screening with Ex-Post Participation Constraints" (2017). Cowles Foundation Discussion Papers. 2548.