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Fair Stable Matching: A Nash Social Welfare Approach — arXiv:2609.02354

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.02354
License (as archived): CC0-1.0
Archived: 2026-10-17T03:37:52.518Z
SHA-256 of the archived text: fd3f3acd2866df973951c01fe0b070472e3313eb64bb5756885a84db183eb149
Stable URL of this page: https://metraipolis.com/documento/dc_ff7bb38018be

How to cite

Fair Stable Matching: A Nash Social Welfare Approach — arXiv:2609.02354 — arXiv (en), https://arxiv.org/abs/2609.02354 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ff7bb38018be (Metraipolis archive dc_ff7bb38018be, sha256 fd3f3acd2866df973951c01fe0b070472e3313eb64bb5756885a84db183eb149)

BibTeX

@misc{dcff7bb38018be,
  title = {Fair Stable Matching: A Nash Social Welfare Approach — arXiv:2609.02354},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.02354},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ff7bb38018be; sha256 fd3f3acd2866df973951c01fe0b070472e3313eb64bb5756885a84db183eb149},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.02354. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

While traditional stable matching algorithms, such as the Gale-Shapley algorithm, prioritize stability, they may fall short of achieving equitable outcomes among participants. We study the role of \emph{Nash social welfare} (NSW) as a fairness objective in the classic \emph{stable marriage problem}. We develop \texttt{SNSW-Alg} that finds a stable matching that maximizes Nash social welfare under rank-induced utilities in $\tilde{\mathcal{O}}(n^4)$ time, where $n$ is the number of men or women. We demonstrate that \texttt{SNSW-Alg} balances equity while preserving stability. We empirically evaluate our methods across diverse preference distributions, demonstrating significant gains in fairness without substantial losses in other key measures such as regret, egalitarian criterion, and sex equality. Our findings suggest that the stable matching produced by \texttt{SNSW-Alg} is statistically Pareto-undominated by stable matchings based on other fairness measures - regret, egalitarian, and sex equality. This study offers compelling insights for designing fair-stable matching.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-03 in cs.AI).
Categorie arXiv: Computer Science and Game Theory (cs.GT) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2609.02354 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T03:13:12.540Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-03?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).