Progressive Participation

Abstract

A single seller faces a sequence of buyers with unit demand. The buyers are forward-looking and long-lived but vanish (and are replaced) at a constant rate. The arrival time and the valuation is private information of each buyer and unobservable to the seller. Any incentive compatible mechanism has to induce truth-telling about the arrival time and the evolution of the valuation. We derive the optimal stationary mechanism in closed form and characterize its qualitative structure. As the arrival time is private information, the buyer can choose the time at which he reports his arrival. The truth-telling constraint regarding the arrival time can be represented as an optimal stopping problem. The stopping time determines the time at which the buyer decides to participate in the mechanism. The resulting value function of each buyer cannot be too convex and must be continuously differentiable everywhere, reflecting the option value of delaying participation. The optimal mechanism thus induces progressive participation by each buyer: he participates either immediately or at a future random time.

Keywords: Dynamic Mechanism Design, Interim Incentive Constraints, Interim Participation Constraints, Observable Arrival, Option value, Progressive Participation, Repeated Sales, Stopping Problem, Unobservable Arrival

JEL Classification: D44, D82, D83