IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02932135.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: https://hal.science/hal-02932135/document
    Download Restriction: no
    File URL: https://libkey.io/10.1016/j.artint.2020.103357?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
    2. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    3. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    4. 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.
    5. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    6. Morrill, Thayer, 2010. "The roommates problem revisited," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1739-1756, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Duv{s}an Knop & v{S}imon Schierreich, 2023. "Host Community Respecting Refugee Housing," Papers 2302.13997, arXiv.org, revised Mar 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
    2. Combe, Julien, 2022. "Matching with ownership," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    3. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 431-452, November.
    4. Agnes Cseh & Tamas Fleiner & Petra Harjan, 2020. "Pareto optimal coalitions of fixed size," CERS-IE WORKING PAPERS 2005, Institute of Economics, Centre for Economic and Regional Studies.
    5. Gianpiero Monaco & Luca Moscardelli & Yllka Velaj, 2021. "Additively Separable Hedonic Games with Social Context," Games, MDPI, vol. 12(3), pages 1-14, September.
    6. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    7. Fan-Chin Kung, 2010. "Coalition formation with local public goods and group-size effect," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 573-583, October.
    8. Martin Gairing & Rahul Savani, 2019. "Computing Stable Outcomes in Symmetric Additively Separable Hedonic Games," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1101-1121, August.
    9. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    10. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
    11. Koji Takamiya, 2013. "Coalitional unanimity versus strategy-proofness in coalition formation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 115-130, February.
    12. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    13. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.
    14. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 505-519, April.
    15. Dimitrov, Dinko & Lazarova, Emiliya A., 2008. "Coalitional Matchings," Coalition Theory Network Working Papers 37523, Fondazione Eni Enrico Mattei (FEEM).
    16. Dinko Dimitrov & Emiliya A. Lazarova & Shao-Chin Sung, 2016. "Inducing stability in hedonic games," University of East Anglia School of Economics Working Paper Series 2016-09, School of Economics, University of East Anglia, Norwich, UK..
    17. Barbera, Salvador & Gerber, Anke, 2003. "On coalition formation: durable coalition structures," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 185-203, April.
    18. Papai, Szilvia, 2004. "Unique stability in simple coalition formation games," Games and Economic Behavior, Elsevier, vol. 48(2), pages 337-354, August.
    19. Desmet, Klaus & Le Breton, Michel & Ortuno-Ortin, Ignacio, 2006. "Nation Formation and Genetic Diversity," IDEI Working Papers 133, Institut d'Économie Industrielle (IDEI), Toulouse.
    20. Emiliya Lazarova & Dinko Dimitrov, 2013. "Status-seeking in hedonic games with heterogeneous players," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(4), pages 1205-1229, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-02932135. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.