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Computational Complexity of Hedonic Games on Sparse Graphs

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PRIMA 2019: Principles and Practice of Multi-Agent Systems (PRIMA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11873))

Abstract

The additively separable hedonic game (ASHG) is a model of coalition formation games on graphs. In this paper, we intensively and extensively investigate the computational complexity of finding several desirable solutions, such as a Nash stable solution, a maximum utilitarian solution, and a maximum egalitarian solution in ASHGs on sparse graphs including bounded-degree graphs, bounded-treewidth graphs, and near-planar graphs. For example, we show that finding a maximum egalitarian solution is weakly NP-hard even on graphs of treewidth 2, whereas it can be solvable in polynomial time on trees. Moreover, we give a pseudo fixed parameter algorithm when parameterized by treewidth.

A full version of the paper is available in [13]. This work was partially supported by JSPS KAKENHI Grant Numbers JP17K19960, 17H01698, 19K21537.

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Authors and Affiliations

  1. Department of Information and System Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan

    Tesshu Hanaka

  2. Graduate School of Informatics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan

    Hironori Kiya, Yasuhide Maei & Hirotaka Ono

Authors
  1. Tesshu Hanaka
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  2. Hironori Kiya
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  3. Yasuhide Maei
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  4. Hirotaka Ono
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Corresponding authors

Correspondence to Tesshu Hanaka or Yasuhide Maei .

Editor information

Editors and Affiliations

  1. Università degli Studi di Torino, Turin, Italy

    Matteo Baldoni

  2. Utrecht University, Utrecht, The Netherlands

    Mehdi Dastani

  3. Zhejiang University, Hangzhou, China

    Beishui Liao

  4. National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

    Yuko Sakurai

  5. University of Texas at Dallas, Richardson, TX, USA

    Rym Zalila Wenkstern

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Hanaka, T., Kiya, H., Maei, Y., Ono, H. (2019). Computational Complexity of Hedonic Games on Sparse Graphs. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham. https://doi.org/10.1007/978-3-030-33792-6_43

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  • DOI: https://doi.org/10.1007/978-3-030-33792-6_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33791-9

  • Online ISBN: 978-3-030-33792-6

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