Abstract
We present characterizations of the minimal and the maximal transfer rules by imposing various axioms specifying how a rule should respond to changes in the waiting cost or population. Together with basic axioms, the minimal transfer rule is the only rule satisfying independence of preceding costs, or negative cost monotonicity and last-agent equal responsibility, or balanced consistency, or balanced cost reduction. On the other hand, the maximal transfer rule is the only rule satisfying independence of following costs, or positive cost monotonicity and first-agent equal responsibility, or balanced consistency under constant completion time.
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Notes
- 1.
- 2.
Instead of Pareto indifference, Maniquet (2003) imposes anonymity, which requires that relabeling of agents should not affect the allocation chosen by a rule. Since the same result can be obtained by imposing Pareto indifference (with the same proof), we impose Pareto indifference here.
- 3.
This property states that the effect of player i leaving the game on the payoff of player j ≠i is equal to the effect of player j leaving the game on the payoff of player i.
- 4.
Note that in the balanced contributions property introduced by Myerson (1980) for cooperative games with a restricted set of feasible coalitions, the player set is fixed.
- 5.
Note the difference with the end of the proof of Theorem 4.3. In the proof of Theorem 4.4, we need to make sure to choose all efficient queues, and for any efficient queue, we have the desired formula. In the induction proof of Theorem 4.3, one efficient queue is chosen already from the beginning.
- 6.
See Thomson (1995) for a survey.
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Chun, Y. (2016). Independence, Monotonicity, and Balanced Consistency. In: Fair Queueing. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-319-33771-5_4
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