Clay Thomas, Princeton University

Abstract

Large real-world stable matching markets typically have the property that "the core is small". That is, there are "few" distinct stable matchings, and most agents have unique partners across all stable matchings.  This has important strategic and market design implications. The first theoretical explanation of this phenomenon was presented in [IM]. Namely, the preference lists of agents are short in practice. A later work [AKL] presented another explanation: the imbalance in the number of agents on each side of the market (and the resulting competition) leads to a small core. In this talk, we will review some basic notions of stable matching markets, including the relevance of the "small core" phenomenon. Then, we will prove (simplified versions of) the main results of [IM] and [AKL]. For the latter, we will follow the analysis of [CT], which uses ideas similar to those in [IM].

Depending on time and interest, we may very briefly discuss models between these two papers [KMQ] or plausible random markets where the core is large [R].

[IM] Immorlica and Mahdian. "Incentives in large random two-sided markets." ACM Transactions on Economics and Computation (TEAC) 3.3 (2015): 1-25. (Original version: "Marriage, honesty, and stability", SODA 2005.)

[AKL] Ashlagi, Itai, Yash Kanoria, and Jacob D. Leshno. "Unbalanced random matching markets: The stark effect of competition." Journal of Political Economy 125.1 (2017): 69-98. (Extended abstract in EC 13).

[CT] Cai and Thomas. The Short-Side Advantage in Random Matching Markets. Preprint available at http://clathomasprime.github.io/papers/ShortSideAdvantage.pdf, 2019.

[KMQ] Kanoria, Min, and Qian. "Which Random Matching Markets Exhibit a Stark Effect of Competition?." arXiv preprint https://arxiv.org/abs/2006.14653, 2020.

[R] Ross Rheingans-Yoo. Large random matching markets with localized preference structures can exhibit large cores. Preprint available at https://static.rossry.net/papers/working/ps-core.pdf, 2020.