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Pareto optimality in coalition formation

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  • Aziz, Haris
  • Brandt, Felix
  • Harrenstein, Paul

Abstract

A minimal requirement on allocative efficiency in the social sciences is Pareto optimality. In this paper, we identify a close structural connection between Pareto optimality and perfection that has various algorithmic consequences for coalition formation. Based on this insight, we formulate the Preference Refinement Algorithm (PRA) which computes an individually rational and Pareto optimal outcome in hedonic coalition formation games. Our approach also leads to various results for specific classes of hedonic games. In particular, we show that computing and verifying Pareto optimal partitions in general hedonic games, anonymous games, three-cyclic games, room-roommate games and B-hedonic games is intractable while both problems are tractable for roommate games, W-hedonic games, and house allocation with existing tenants.

Suggested Citation

  • Aziz, Haris & Brandt, Felix & Harrenstein, Paul, 2013. "Pareto optimality in coalition formation," Games and Economic Behavior, Elsevier, vol. 82(C), pages 562-581.
    • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:562-581
    DOI: 10.1016/j.geb.2013.08.006
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    Citations

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    Cited by:

    1. Niclas Boehmer & Edith Elkind, 2020. "Stable Roommate Problem with Diversity Preferences," Papers 2004.14640, arXiv.org.
    2. Bugra Caskurlu & Fatih Erdem Kizilkaya, 2022. "On Hedonic Games with Common Ranking Property," Papers 2205.11939, arXiv.org.
    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. Aziz, Haris & Brandl, Florian, 2022. "The vigilant eating rule: A general approach for probabilistic economic design with constraints," Games and Economic Behavior, Elsevier, vol. 135(C), pages 168-187.
    5. Ágnes Cseh & Tamás Fleiner & Petra Harján, 2019. "Pareto Optimal Coalitions of Fixed Size," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 4(1), pages 87-108, November.
    6. Aziz, Haris & Brandl, Florian & Brandt, Felix, 2015. "Universal Pareto dominance and welfare for plausible utility functions," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 123-133.
    7. Aziz, Haris & Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2017. "Computational aspects of assigning agents to a line," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 93-99.
    8. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    9. Andreas Darmann, 2018. "Stable and Pareto optimal group activity selection from ordinal preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1183-1209, November.
    10. Combe, Julien, 2022. "Matching with ownership," Journal of Mathematical Economics, Elsevier, vol. 98(C).
    11. 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.
    12. Haris Aziz, 2016. "A generalization of the AL method for fair allocation of indivisible objects," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 307-324, October.
    13. 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.
    14. Andreas Darmann & Edith Elkind & Sascha Kurz & Jérôme Lang & Joachim Schauer & Gerhard Woeginger, 2018. "Group activity selection problem with approval preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 767-796, September.
    15. Rothe, Jörg & Schadrack, Hilmar & Schend, Lena, 2018. "Borda-induced hedonic games with friends, enemies, and neutral players," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 21-36.

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    More about this item

    Keywords

    Coalition formation; Hedonic games; Pareto optimality; Computational complexity;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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