The Scope of Sequential Screening with Ex-Post Participation Constraints

We study the classic sequential screening problem in the presence of ex-post participation constraints. We establish necessary and sufficient conditions that determine exhaustively when the optimal selling mechanism is either static or sequential. In the static contract, the buyers are not screened with respect to their interim type and the object is sold at a posted price. In the sequential contract, the buyers are screened with respect to their interim type and a menu of quantities is offered. 

We completely characterize the optimal sequential contract with binary interim types and a continuum of ex-post values. Importantly, the optimal sequential contract randomizes the allocation of the low type buyer while giving a deterministic allocation to the high type. Finally, we provide additional results for the case of multiple interim types.