Placement With Assignment Guarantees and Semi-Flexible Capacities

Orhan Aygün () and Günnur Ege Bilgin ()

CRC TR 224 Discussion Paper Series from University of Bonn and University of Mannheim, Germany

Abstract: We analyze an extension of the many-to-one placement problem, where some doctors are exogenously guaranteed a seat at a program, which defines a lower bound on their assignment. Respecting assignment guarantees, combined with the limited capacities of programs often violates fairness and leaves more preferred doctors unemployed. In pursuance of restoring fairness, a designer often has to deviate from the target capacities of programs, and imposing the traditional notion of fairness results in excessive deviations from the target capacities. In order to prevent excessive deviations, we introduce two notions that are tailored to the environment: q-fairness and avoiding unnecessary slots. Furthermore, we introduce the Assignment-Guarantees-Adjusted Mechanism (AGAM) and show that it is the unique strategy-proof mechanism that satisfies q-fairness and avoids unnecessary slots whilst respecting assignment guarantees. Furthermore, among the mechanisms that satisfy q-fairness and respect guarantees, AGAM minimizes the deviation from the target capacities.

Keywords: many-to-one matching; assignment guarantees; flexible capacities; q-fairness (search for similar items in EconPapers)
JEL-codes: C78 D47 D78 D82 (search for similar items in EconPapers)
Pages: 30
Date: 2023-04
New Economics Papers: this item is included in nep-des
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