Allocation with Weak Priorities and General Constraints

Abstract

Allocating scarce resources with (weak) priority and complex constraints has many applications ranging from course allocation, and healthcare rationing to refugee resettlement. Its generality, however, mostly leads to impossibility results. We offer a positive result with a mechanism based on a new concept called competitive stable equilibrium. This is a natural extension of competitive equilibrium with endowed budgets that accommodates weak priorities. Specifically, an agent only needs to pay for a resource if it belongs to the last tier among the agents currently consuming the resource. This concept applies to both frameworks of one-sided and two-sided markets in a unifying way and allows for a more flexible tie-breaking rule by giving agents different budgets. We empirically apply our mechanism to reassign season tickets to families in the presence of social distancing. Our simulation results show that our method outperforms existing ones in both efficiency and fairness measures.