IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v307y2023i2p773-784.html
   My bibliography  Save this article

Computing welfare-Maximizing fair allocations of indivisible goods

Author

Listed:
  • Aziz, Haris
  • Huang, Xin
  • Mattei, Nicholas
  • Segal-Halevi, Erel

Abstract

We analyze the run-time complexity of computing allocations that are both fair and maximize the utilitarian social welfare, defined as the sum of agents’ utilities. We focus on two tractable fairness concepts: envy-freeness up to one item (EF1) and proportionality up to one item (PROP1). We consider two computational problems: (1) Among the utilitarian-maximal allocations, decide whether there exists one that is also fair; (2) among the fair allocations, compute one that maximizes the utilitarian welfare. We show that both problems are strongly NP-hard when the number of agents is variable, and remain NP-hard for a fixed number of agents greater than two. For the special case of two agents, we find that problem (1) is polynomial-time solvable, while problem (2) remains NP-hard. Finally, with a fixed number of agents, we design pseudopolynomial-time algorithms for both problems. We extend our results to the stronger fairness notions envy-freeness up to any item (EFx) and proportionality up to any item (PROPx).

Suggested Citation

  • Aziz, Haris & Huang, Xin & Mattei, Nicholas & Segal-Halevi, Erel, 2023. "Computing welfare-Maximizing fair allocations of indivisible goods," European Journal of Operational Research, Elsevier, vol. 307(2), pages 773-784.
    • Handle: RePEc:eee:ejores:v:307:y:2023:i:2:p:773-784
    DOI: 10.1016/j.ejor.2022.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722007822
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.10.013?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Nick Arnosti & Peng Shi, 2020. "Design of Lotteries and Wait-Lists for Affordable Housing Allocation," Management Science, INFORMS, vol. 66(6), pages 2291-2307, June.
    3. Agnetis, Alessandro & Chen, Bo & Nicosia, Gaia & Pacifici, Andrea, 2019. "Price of fairness in two-agent single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 276(1), pages 79-87.
    4. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    5. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, vol. 102(5), pages 2237-2271, August.
    6. Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2017. "Price of Fairness for allocating a bounded resource," European Journal of Operational Research, Elsevier, vol. 257(3), pages 933-943.
    7. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    8. Sascha Kurz, 2016. "The Price of Fairness for a Small Number of Indivisible Items," Operations Research Proceedings, in: Marco Lübbecke & Arie Koster & Peter Letmathe & Reinhard Madlener & Britta Peis & Grit Walther (ed.), Operations Research Proceedings 2014, edition 1, pages 335-340, Springer.
    9. Siddharth Barman & Sanath Kumar Krishnamurthy & Rohit Vaish, 2018. "Greedy Algorithms for Maximizing Nash Social Welfare," Papers 1801.09046, arXiv.org.
    10. Simina Br^anzei & Fedor Sandomirskiy, 2019. "Algorithms for Competitive Division of Chores," Papers 1907.01766, arXiv.org, revised Jul 2023.
    11. Erbeyoğlu, Gökalp & Bilge, Ümit, 2020. "A robust disaster preparedness model for effective and fair disaster response," European Journal of Operational Research, Elsevier, vol. 280(2), pages 479-494.
    12. Dan A. Iancu & Nikolaos Trichakis, 2014. "Fairness and Efficiency in Multiportfolio Optimization," Operations Research, INFORMS, vol. 62(6), pages 1285-1301, December.
    13. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    14. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
    15. Jagtenberg, C.J. & Mason, A.J., 2020. "Improving fairness in ambulance planning by time sharing," European Journal of Operational Research, Elsevier, vol. 280(3), pages 1095-1107.
    16. Rajeev Kohli & R. Sukumar, 1990. "Heuristics for Product-Line Design Using Conjoint Analysis," Management Science, INFORMS, vol. 36(12), pages 1464-1478, December.
    17. Karaenke, Paul & Bichler, Martin & Merting, Soeren & Minner, Stefan, 2020. "Non-monetary coordination mechanisms for time slot allocation in warehouse delivery," European Journal of Operational Research, Elsevier, vol. 286(3), pages 897-907.
    18. Kilgour, D. Marc & Vetschera, Rudolf, 2018. "Two-player fair division of indivisible items: Comparison of algorithms," European Journal of Operational Research, Elsevier, vol. 271(2), pages 620-631.
    Full references (including those not matched with items on IDEAS)

    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. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    2. Eirinakis, Pavlos & Mourtos, Ioannis & Zampou, Eleni, 2022. "Random Serial Dictatorship for horizontal collaboration in logistics," Omega, Elsevier, vol. 111(C).
    3. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 33(4), pages 541-571.
    4. Argyris, Nikolaos & Karsu, Özlem & Yavuz, Mirel, 2022. "Fair resource allocation: Using welfare-based dominance constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 560-578.
    5. Akoluk, Damla & Karsu, Özlem, 2022. "Ensuring multidimensional equality in public service," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    6. David Rea & Craig Froehle & Suzanne Masterson & Brian Stettler & Gregory Fermann & Arthur Pancioli, 2021. "Unequal but Fair: Incorporating Distributive Justice in Operational Allocation Models," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 2304-2320, July.
    7. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202103100800001123, Iowa State University, Department of Economics.
    8. Eric Budish & Gérard P. Cachon & Judd B. Kessler & Abraham Othman, 2017. "Course Match: A Large-Scale Implementation of Approximate Competitive Equilibrium from Equal Incomes for Combinatorial Allocation," Operations Research, INFORMS, vol. 65(2), pages 314-336, April.
    9. Pamela Giustinelli & Charles F. Manski, 2018. "Survey Measures Of Family Decision Processes For Econometric Analysis Of Schooling Decisions," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 81-99, January.
    10. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    11. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    12. Ortega, Josué, 2020. "Multi-unit assignment under dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 15-24.
    13. Gudmundsson, Jens & Hougaard, Jens Leth & Platz, Trine Tornøe, 2023. "Decentralized task coordination," European Journal of Operational Research, Elsevier, vol. 304(2), pages 851-864.
    14. Agnetis, Alessandro & Chen, Bo & Nicosia, Gaia & Pacifici, Andrea, 2019. "Price of fairness in two-agent single-machine scheduling problems," European Journal of Operational Research, Elsevier, vol. 276(1), pages 79-87.
    15. Antonio Romero-Medina & Matteo Triossi, 2017. "(Group) Strategy-proofness and stability in many-to many marching markets," Documentos de Trabajo 332, Centro de Economía Aplicada, Universidad de Chile.
    16. Xia Chen & Yucheng Dong & Ying He, 2024. "Group Risky Choice and Resource Allocation Under Social Comparison Effects," Group Decision and Negotiation, Springer, vol. 33(5), pages 977-1017, October.
    17. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    18. Miralles, Antonio & Pycia, Marek, 2021. "Foundations of pseudomarkets: Walrasian equilibria for discrete resources," Journal of Economic Theory, Elsevier, vol. 196(C).
    19. Mireille Ducassé & Peggy Cellier, 2016. "Using Bids, Arguments and Preferences in Sensitive Multi-unit Assignments: A p-Equitable Process and a Course Allocation Case Study," Group Decision and Negotiation, Springer, vol. 25(6), pages 1211-1235, November.
    20. Triossi, Matteo, 2018. "Centralized Course Allocation," UC3M Working papers. Economics 27388, Universidad Carlos III de Madrid. Departamento de Economía.

    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:eee:ejores:v:307:y:2023:i:2:p:773-784. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.