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Maximizing Utilitarian and Egalitarian Welfare of Fractional Hedonic Games on Tree-Like Graphs

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14461))

Abstract

Fractional hedonic games are coalition formation games where the utility of a player is determined by the average value they assign to the members of their coalition. These games are a variation of graph hedonic games, which are a class of coalition formation games that can be succinctly represented. Due to their applicability in network clustering and their relationship to graph hedonic games, fractional hedonic games have been extensively studied from various perspectives. However, finding welfare-maximizing partitions in fractional hedonic games is a challenging task due to the nonlinearity of utilities. In fact, it has been proven to be NP-hard in general and can be solved in polynomial time only for a limited number of graph classes, such as trees. This paper presents (pseudo)polynomial-time algorithms to compute welfare-maximizing partitions in fractional hedonic games on tree-like graphs. We consider two types of social welfare measures: utilitarian and egalitarian. Tree-like graphs refer to graphs with bounded treewidth and block graphs. An NP-hardness result demonstrates that the pseudopolynomial-time solvability is the best possible under the assumption P \(\ne \) NP.

Partially supported by JSPS KAKENHI Grant Numbers JP20H05967, JP21H05852, JP21K17707, JP21K19765, JP22H00513, and JP23H04388.

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Authors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Tesshu Hanaka

  2. Nagoya University, Nagoya, Japan

    Airi Ikeyama & Hirotaka Ono

Authors
  1. Tesshu Hanaka
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  2. Airi Ikeyama
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  3. Hirotaka Ono
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Corresponding author

Correspondence to Tesshu Hanaka .

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Editors and Affiliations

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

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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Hanaka, T., Ikeyama, A., Ono, H. (2024). Maximizing Utilitarian and Egalitarian Welfare of Fractional Hedonic Games on Tree-Like Graphs. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14461. Springer, Cham. https://doi.org/10.1007/978-3-031-49611-0_28

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  • DOI: https://doi.org/10.1007/978-3-031-49611-0_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49610-3

  • Online ISBN: 978-3-031-49611-0

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