Optimal Dynamic Allocation: Simplicity through Information Design

Abstract

We study mechanism design in dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasi-linear in her waiting cost. Social welfare is defined as the agents’ average payoff. We consider a general class of mechanisms that determine the joint distribution of the object assigned to each agent and the agent’s waiting time. We identify the welfare-maximizing mechanism and show that it can be implemented by a simple policy when the market maker can design the information disclosed about the objects: by a first-come, first-served waitlist that allows agents to accept or decline offers paired with an information disclosure scheme that pools adjacent object types. From a technical perspective, standard ironing techniques in mechanism design are not directly applicable, due to the concurrence of two complicating factors: the supermodularity of the agents’ values for objects and the capacity constraints of the heterogeneous object types. We take a different approach by characterizing the set of monotone, non-wasteful, and implementable interim allocation rules through a majorization condition, using the Bauer’s Maximum Principle [Bauer, 1958] to show that the optimal rule is an extreme point of this set, and then applying the extreme point characterization results of Kleiner et al. [2020].

JEL Classification: C78, D47