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Random Matching Markets with Correlated Preferences

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  • Bill Wang

Abstract

In the Gale-Shapley model of two-sided matching, it is well known that for generic preferences, the outcomes for each side can vary dramatically in the male-optimal vs. female-optimal stable matchings. In this paper, we show that under a widely used characterization of similarity in rankings, even a weak correlation in preferences guarantees assortative matching with high probability as the market size tends to infinity. It follows that the men's average ranking of women and the women's average ranking of men are asymptotically equivalent in all stable matchings with high probability, as long as the market imbalance is not too extreme.

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  • Bill Wang, 2026. "Random Matching Markets with Correlated Preferences," Papers 2603.24526, arXiv.org.
    • Handle: RePEc:arx:papers:2603.24526
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    References listed on IDEAS

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    1. James W. Boudreau & Vicki Knoblauch, 2010. "Marriage Matching and Intercorrelation of Preferences," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 12(3), pages 587-602, June.
    2. Itai Ashlagi & Yash Kanoria & Jacob D. Leshno, 2017. "Unbalanced Random Matching Markets: The Stark Effect of Competition," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 69-98.
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    4. Holzman, Ron & Samet, Dov, 2014. "Matching of like rank and the size of the core in the marriage problem," Games and Economic Behavior, Elsevier, vol. 88(C), pages 277-285.
    5. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
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