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Tiered Random Matching Markets: Rank Is Proportional to Popularity

Authors Itai Ashlagi, Mark Braverman, Amin Saberi, Clayton Thomas, Geng Zhao

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Author Details

Itai Ashlagi
  • Department of Management Science and Engineering, Stanford University, CA, USA
Mark Braverman
  • Department of Computer Science, Princeton University, NJ, USA
Amin Saberi
  • Department of Management Science and Engineering, Stanford University, CA, USA
Clayton Thomas
  • Department of Computer Science, Princeton University, NJ, USA
Geng Zhao
  • Department of Computer Science, Stanford University, CA, USA

Funding

  • Braverman, Mark: Research supported in part by the NSF Alan T. Waterman Award, Grant No. 1933331, a Packard Fellowship in Science and Engineering, and the Simons Collaboration on Algorithms and Geometry. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.

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Itai Ashlagi, Mark Braverman, Amin Saberi, Clayton Thomas, and Geng Zhao. Tiered Random Matching Markets: Rank Is Proportional to Popularity. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 46:1-46:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITCS.2021.46

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory and mechanism design
Keywords
  • Stable matching
  • stable marriage problem
  • tiered random markets
  • deferred acceptance

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References

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