Optimal Dynamic Allocation

The paper presented in this Virtual Market Design Seminar studies dynamic nonmonetary markets where objects are allocated to unit-demand agents with private types; such as in the allocation of public housing or deceased-donor organs. An agent’s value for an object is supermodular in her type and the quality of the object, and her payoff is quasilinear in her waiting cost. The social planner's objective is a linear combination of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). The authors identify the optimal mechanism in the class of direct-revelation mechanisms that elicit agents’ types and assign them to objects over time. The presented paper shows that, when the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the information disclosed about each object is an interval containing the object quality, rather than the exact quality. These intervals partition the quality space. The authors also show that when the planner's objective weight on welfare increases, these intervals become coarser, and optimal disclosure policies less informative. A direct corollary is that mechanisms that achieve higher welfare also induce lower distributional inequality, in terms of the Lorenz order.