Matchings under Preferences: Strength of Stability and Tradeoffs

Jiehua Chen, Piotr Skowron, Manuel Sorge

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We propose two solution concepts for matchings under preferences: Robustness and near stability. The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of tradeoffs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined tradeoffs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching (if it exists), and we prove that finding a socially optimal and nearly stable matching is computationally hard.

Original languageEnglish
Article number3485000
JournalACM Transactions on Economics and Computation
Volume9
Issue number4
DOIs
StatePublished - 1 Dec 2021
Externally publishedYes

Keywords

  • NP-hardness
  • Stable matchings
  • approximation algorithms
  • concepts of stability
  • exact algorithms
  • parameterized complexity analysis

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Economics and Econometrics
  • Marketing
  • Computational Mathematics

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