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Cutoff stability under distributional constraints with an application to summer internship matching

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  • Haris Aziz
  • Anton Baychkov
  • Peter Biro

Abstract

We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

Suggested Citation

  • Haris Aziz & Anton Baychkov & Peter Biro, 2021. "Cutoff stability under distributional constraints with an application to summer internship matching," Papers 2102.02931, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2102.02931
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    Cited by:

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    3. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202104130700001123, Iowa State University, Department of Economics.
    4. Cho, Sung-Ho & Koshimura, Miyuki & Mandal, Pinaki & Yahiro, Kentaro & Yokoo, Makoto, 2022. "Impossibility of weakly stable and strategy-proof mechanism," Economics Letters, Elsevier, vol. 217(C).
    5. Orhan Aygün & Bertan Turhan, 2023. "How to De-Reserve Reserves: Admissions to Technical Colleges in India," Management Science, INFORMS, vol. 69(10), pages 6147-6164, October.

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