×

Stable and extremely unequal. (English) Zbl 1521.91246

Summary: We show how stability as a solution concept in matching often comes at the cost of extreme forms on inequality. Restricting our attention to aligned preferences, we show that the stable matching results from the lexicographic welfare maximization of the pairs’ welfare, starting with the best-off. We compare this solution with an alternative allocation, that although unstable, maximizes the welfare lexicographically starting with the worst-off pairs.

MSC:

91B68 Matching models

References:

[1] Ashlagi, I.; Kanoria, Y.; Leshno, J. D., Unbalanced random matching markets: The stark effect of competition, J. Polit. Econ., 125, 69-98 (2017)
[2] Banerjee, S.; Konishi, H.; Sönmez, T., Core in a simple coalition formation game, Soc. Choice Welf., 18, 135-153 (2001) · Zbl 1069.91504
[3] Burkard, R.; Dell’Amico, M.; Martello, S., Assignment Problems (2009), SIAM · Zbl 1196.90002
[4] Cantillon, E.; Chen, L.; Pereyra, J., Respecting priorities versus respecting preferences in school choice: When is there a trade-off? (2022), arXiv:2212.02881
[5] Clark, S., The uniqueness of stable matchings, Contrib. Theor. Econ., 6, 1-28 (2006)
[6] Eeckhout, J., On the uniqueness of stable marriage matchings, Econ. Lett., 69, 1-8 (2000) · Zbl 0960.91052
[7] Gale, D.; Shapley, L., College admissions and the stability of marriage, Amer. Math. Monthly, 69, 9-15 (1962) · Zbl 0109.24403
[8] Ghelfi, O.; Vladu, A., Lexicographically optimal matchings in bipartite graphs (2023), preprint
[9] Gusfield, D.; Irving, R., The Stable Marriage Problem, Structure and Algorithms (1989), MIT Press · Zbl 0703.68046
[10] Irving, R.; Kavitha, T.; Mehlhorn, K.; Michail, D.; Paluch, K., Rank-maximal matchings, ACM Trans. Algorithm., 2, 602-610 (2006) · Zbl 1321.90116
[11] Kojima, F.; Manea, M., Axioms for deferred acceptance, Econometrica, 78-2, 633-653 (2010) · Zbl 1229.91246
[12] Niederle, M., Yariv, L., 2009. Decentralized matching with aligned preferences. NBER Working Paper 14840.
[13] Pycia, M., Stability and preference alignment in matching and coalition formation, Econometrica, 80, 323-362 (2012) · Zbl 1274.91332
[14] Shapley, G.; Scarf, H., On cores and indivisibility, J. Math. Econom., 1, 23-37 (1974) · Zbl 0281.90014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.