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Computational Complexity of k-Stable Matchings

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Algorithmic Game Theory (SAGT 2023)

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Abstract

We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching k-stable if no other matching exists that is more beneficial to at least k out of the n agents. The concept generalizes the recently studied majority stability (Thakur, 2021). We prove that whereas the verification of k-stability for a given matching is polynomial-time solvable in all three models, the complexity of deciding whether a k-stable matching exists depends on \(\frac{k}{n}\) and is characteristic to each model.

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Acknowledgments

We thank Barton E. Lee for drawing our attention to the concept of majority stability and for producing thought-provoking example instances. We also thank the reviewers of the paper for their suggestions that helped improving the presentation of the paper. Haris Aziz acknowledges the support from NSF-CSIRO grant on ‘Fair Sequential Collective Decision-Making’. Gergely Csáji acknowledges the financial support by the Hungarian Academy of Sciences, Momentum Grant No. LP2021-1/2021, and by the Hungarian Scientific Research Fund, OTKA, Grant No. K143858. Ágnes Cseh’s work was supported by OTKA grant K128611 and the János Bolyai Research Fellowship.

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Authors and Affiliations

  1. UNSW Sydney, Sydney, Australia

    Haris Aziz

  2. Eötvös Loránd University, Budapest, Hungary

    Gergely Csáji

  3. Institute of Economics, Centre for Economic and Regional Studies, Budapest, Hungary

    Gergely Csáji & Ágnes Cseh

  4. University of Bayreuth, Bayreuth, Germany

    Ágnes Cseh

Authors
  1. Haris Aziz
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  2. Gergely Csáji
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  3. Ágnes Cseh
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Correspondence to Ágnes Cseh .

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Editors and Affiliations

  1. Royal Holloway University of London, Egham, UK

    Argyrios Deligkas

  2. University of Edinburgh, Edinburgh, UK

    Aris Filos-Ratsikas

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Aziz, H., Csáji, G., Cseh, Á. (2023). Computational Complexity of k-Stable Matchings. In: Deligkas, A., Filos-Ratsikas, A. (eds) Algorithmic Game Theory. SAGT 2023. Lecture Notes in Computer Science, vol 14238. Springer, Cham. https://doi.org/10.1007/978-3-031-43254-5_18

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  • DOI: https://doi.org/10.1007/978-3-031-43254-5_18

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