Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems

A set of agents with different waiting costs have to receive a service of equal length of time from a single provider which can serve only one agent at a time. One needs to form a queue and set up monetary transfers to compensate the agents who have to wait. We analyze rules that are efficient, fair, and immune to strategic behavior. We prove that no rule is Pareto-efficient and coalitional strategyproof. We also show that in combination with Pareto-efficiency and strategy-proofness, equal treatment of equals is equivalent to no-envy. We identify the class of rules that satisfy Pareto-efficiency, equal treatment of equals, and strategy-proofness. Among multi-valued rules, there is a unique rule that satisfies Pareto-efficiency, anonymity, and strategy-proofness. JEL Classification: D63, C72.