Constrained stability in two-sided matching markets
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Constrained stability in two‑sided matching markets Mustafa Oğuz Afacan1 · Umut Mert Dur2 Received: 25 March 2018 / Accepted: 27 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In two-sided matching markets, not every worker-firm (doctor-hospital) pair can match with each other even if they would rather do so due to possible non-poaching contracts among firms or market specific regulations. Motivated by this observation, we introduce a new matching framework and a constrained stability notion, while emphasizing that the usual matching problem and Gale and Shapley, Am Math Mon 69:9–15 (1962)’s stability notion are realized as special cases of our formulation and the constrained stability notion. We first show that some fundamental properties of the stable matchings do not carry over to the constrained stable matchings. The worker-proposing deferred acceptance (DA) mechanism fails to be worker-optimal constrained stable, yet it is the unique constrained stable and strategy-proof mechanism. Lastly, we propose a worker-optimal constrained stable mechanism that also improves the workers’ welfare upon that under DA.
1 Introduction Stability is one of the most important concerns in matching markets. In one-sided problems, where one side of the market is viewed as objects to be consumed (e.g. school choice), stability is perceived as a fairness property. In two-sided problems, where both sides are agents, such as worker-firm matching, stability is deemed an equilibrium property that rules out every blocking pair, i.e., any unmatched agent pair who would rather match with each other. There is an extensive literature, including Roth (1984, 1991), Roth and Xing (1994), that has documented how a lack of stability in some real-life matching markets has caused them to fail. We thank the editors and the anonymous referees for their comments and suggestions. * Umut Mert Dur [email protected] Mustafa Oğuz Afacan [email protected] 1
Faculty of Arts and Social Sciences, Sabancı University, Orhanlı, Tuzla, 34956 İstanbul, Turkey
2
Poole School of Management, North Carolina State University, Raleigh, NC 27695, USA
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M. O. Afacan, U. M. Dur
The extant literature has already offered particular generalizations of stability. This study takes one step further in that direction and proposes another such generalization, which admits those of Abdulkadiroǧlu (2011), Afacan et al. (2017), and Dur et al. (2018) as its special cases. In the worker-firm matching terminology, stability assumes that any worker-firm pair can match with each other, as long as they want. However, this may not be the case for every matching market. This may be due to non-poaching agreements among firms that prohibit each of those firms from hiring employees from each other or due to market specific regulations.1 For instance, one such market regulation has been in charge in Turkey and prevents doctors who have resigned from public hospitals three times or more from working at public hospitals.2 We can f
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