No-envy in queueing problems

We explore the implications of no-envy (Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiency and no-envy . The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envy together with an additional solidarity requirementhow agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.

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