Equity and Efficiency in Dynamic Matching: Extreme Waitlist Policies

Abstract

Waitlists are commonly used to allocate scarce resources, such as public housing or organs. Waitlist policies attempt to prioritize agents who wait longer by assigning them priority points (à la first come, first served). We show that such point systems can lead to severe inequality across the agents’ assignment probabilities unless they use randomization. In particular, deterministic point systems lead to a more unequal allocation than any other rule that prioritizes earlier arrivals, an axiom that ensures that agents who wait longer are treated (weakly) better. Among the policies abiding by this axiom, we show that service in random order (SIRO) leads to the most equal allocation. From a utilitarian perspective, we show that the planner faces no trade-off between equity and efficiency when the flow utility from waiting is nonnegative or negative and increasing over time. In these cases, SIRO is also the most efficient policy. However, when the flow cost of waiting increases over time, then the planner may face an efficiency–equity trade-off: SIRO remains the most equitable policy but may not be the most efficient one. This paper was accepted by Omar Besbes, revenue management and market analytics.