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Price of Pareto Optimality in hedonic games

Author

Listed:
  • Edith Elkind

    (University of Oxford)

  • Angelo Fanelli

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Michele Flammini

    (GSSI - Gran Sasso Science Institute)

Abstract

The Price of Anarchy measures the welfare loss caused by selfish behavior: it is defined as the ratio of the social welfare in a socially optimal outcome and in a worst Nash equilibrium. Similar measures can be derived for other classes of stable outcomes. We observe that Pareto optimality can be seen as a notion of stability: an outcome is Pareto optimal if and only if it does not admit a deviation by the grand coalition that makes all players weakly better off and some players strictly better off. Motivated by this observation, we introduce the concept of Price of Pareto Optimality: this is an analogue of the Price of Anarchy, with the worst Nash equilibrium replaced with the worst Pareto optimal outcome. We then study this concept in the context of hedonic games, and provide lower and upper bounds on the Price of Pareto Optimality in three classes of hedonic games: additively separable hedonic games, fractional hedonic games, and modified fractional hedonic games. © 2020 Elsevier B.V.

Suggested Citation

  • Edith Elkind & Angelo Fanelli & Michele Flammini, 2020. "Price of Pareto Optimality in hedonic games," Post-Print hal-02932135, HAL.
    • Handle: RePEc:hal:journl:hal-02932135
    DOI: 10.1016/j.artint.2020.103357
    Note: View the original document on HAL open archive server: https://hal.science/hal-02932135
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    References listed on IDEAS

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    3. Vittorio Bilò & Angelo Fanelli & Michele Flammini & Gianpiero Monaco & Luca Moscardelli, 2018. "Nash Stable Outcomes in Fractional Hedonic Games: Existence, Efficiency and Computation," Post-Print hal-02089363, HAL.
    4. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    5. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    6. Morrill, Thayer, 2010. "The roommates problem revisited," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1739-1756, September.
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