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Fast, Fair and Truthful Distributed Stable Matching for Common Preferences

Authors Juho Hirvonen , Sara Ranjbaran

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Author Details

Juho Hirvonen
  • Helsinki Institute for Information Technology HIIT, Finland
  • Department of Computer Science, Aalto University, Espoo, Finland
Sara Ranjbaran
  • Department of Computer Science, Aalto University, Espoo, Finland

Funding

  • Ranjbaran, Sara: Supported by Helsinki Institute for Information Technology HIIT.

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Juho Hirvonen and Sara Ranjbaran. Fast, Fair and Truthful Distributed Stable Matching for Common Preferences. In 28th International Conference on Principles of Distributed Systems (OPODIS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 324, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.OPODIS.2024.30

Abstract

Stable matching is a fundamental problem studied both in economics and computer science. The task is to find a matching between two sides of agents that have preferences over who they want to be matched with. A matching is stable if no pair of agents prefer each other over their current matches. The deferred acceptance algorithm of Gale and Shapley solves this problem in polynomial time. Further, it is a mechanism: the proposing side in the algorithm is always incentivised to report their preferences truthfully.
The deferred acceptance algorithm has a natural interpretation as a distributed algorithm (and thus a distributed mechanism). However, the algorithm is slow in the worst case and it is known that the stable matching problem cannot be solved efficiently in the distributed setting. In this work we study a natural special case of the stable matching problem where all agents on one of the two sides share common preferences. We show that in this case the deferred acceptance algorithm does yield a fast and truthful distributed mechanism for finding a stable matching. We show how algorithms for sampling random colorings can be used to break ties fairly and extend the results to fractional stable matching.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Distributed algorithms
Keywords
  • stable matching
  • deferred acceptance
  • local algorithm
  • mechanism design

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