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Guaranteed size ratio of ordinally efficient and envy-free mechanisms in the assignment problem

Chao Huang and Guoqiang Tian

Games and Economic Behavior, 2017, vol. 105, issue C, 1-8

Abstract: In the assignment problem where agents can stay unassigned, the size of the assignment is an important consideration for designers. Bogomolnaia and Moulin (2015) show that there is a tension between size and fairness: the guaranteed size ratio of any envy-free mechanism is at most rm, which converges decreasingly to 1−1e≈63.2% as the maximum size increases. They then ask whether rm is also the guaranteed size ratio for any ordinally efficient and envy-free mechanism. We study this issue and show that the lower bound of the guaranteed size ratio of ordinally efficient and envy-free mechanisms converges to 12 as the maximum size increases, which means that almost half of the maximum size is wasted at the lower bound. Moreover, the exact lower bound is m+12m when the maximum size m is odd.

Keywords: Size of assignment; Ordinal efficiency; Envy-freeness (search for similar items in EconPapers)
JEL-codes: D63 D70 (search for similar items in EconPapers)
Date: 2017
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