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oai:drops-oai.dagstuhl.de:13585 2024-03-06T10:52:22Z ddc:004 open_access

Tiered Random Matching Markets: Rank Is Proportional to Popularity Ashlagi, Itai Braverman, Mark Saberi, Amin Thomas, Clayton Zhao, Geng Stable matching stable marriage problem tiered random markets deferred acceptance We study the stable marriage problem in two-sided markets with randomly generated preferences. Agents on each side of the market are divided into a constant number of "soft" tiers, which capture agents' qualities. Specifically, every agent within a tier has the same public score, and agents on each side have preferences independently generated proportionally to the public scores of the other side. We compute the expected average rank which agents in each tier have for their partners in the man-optimal stable matching, and prove concentration results for the average rank in asymptotically large markets. Furthermore, despite having a significant effect on ranks, public scores do not strongly influence the probability of an agent matching to a given tier of the other side. This generalizes the results by Pittel [Pittel, 1989], which analyzed markets with uniform preferences. The results quantitatively demonstrate the effect of competition due to the heterogeneous attractiveness of agents in the market. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Itai Ashlagi and Mark Braverman and Amin Saberi and Clayton Thomas and Geng Zhao 2021 Is Part Of LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2021.46 urn:nbn:de:0030-drops-135851 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.46 eng https://creativecommons.org/licenses/by/3.0/legalcode