Abstract
We explore the implications of no-envy (Foley, Yale Econ Essays 7:45–98, 1967) in the context of queueing problems. First, it is not difficult to show that no-envy implies queue-efficiency. Then, we identify an easy way of checking whether a rule satisfies no-envy. The existence of such a rule can easily be established. We also ask whether there is a rule satisfying efficiency and no-envy together with either one of two cost monotonicity axioms, negative cost monotonicity and positive cost monotonicity. However, there is no rule satisfying efficiency, no-envy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envy, and 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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Notes
- 1.
As we show later, if the society consists of only two agents, then the minimal transfer rule satisfies efficiency, no-envy, and negative cost monotonicity, and the maximal transfer rule satisfies efficiency, no-envy, and positive cost monotonicity. Moreover, the rules can be characterized by these axioms if Pareto indifference is additionally imposed. See Remark 5.2 for details.
- 2.
- 3.
Since this is a queue on a single machine, \(\sigma _{i}\neq \sigma _{j}\).
- 4.
Object-efficiency requires that there is no feasible allocation which makes every agent better off and at least one agent strictly better off.
- 5.
Given two groups of the same size, suppose that a group redistributes among its members what is available to the other group. If a rule selects an allocation which is impossible to make every agent in the group better off, with at least one agent strictly better off, even after considering the possibility of redistribution, then the rule satisfies group no-envy.
- 6.
Allocations that can be supported as Walrasian equilibrium with an equal implicit income.
- 7.
For this, a position in a queue is considered as an indivisible good.
- 8.
If Pareto indifference is not imposed, then it is possible to choose only one efficient queue when two agents have equal waiting costs.
- 9.
Note that budget balance is imposed as a part of the feasibility requirement in Bevia (1996).
- 10.
Pareto optimality requires that there is no feasible allocation which makes every agent better off and at least one agent strictly better off.
- 11.
Resource monotonicity requires that an increase in resources should not hurt any agent.
- 12.
For a possibility result, see Alkan et al. (1991).
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Chun, Y. (2016). No-Envy. In: Fair Queueing. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-319-33771-5_5
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DOI: https://doi.org/10.1007/978-3-319-33771-5_5
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