IDEAS home Printed from https://ideas.repec.org/a/spr/grdene/v33y2024i4d10.1007_s10726-024-09885-x.html
   My bibliography  Save this article

Two-Person Fair Division with Additive Valuations

Author

Listed:
  • D. Marc Kilgour

    (Wilfrid Laurier University)

  • Rudolf Vetschera

    (University of Vienna)

Abstract

In the literature, many desirable properties for allocations of indivisible goods have been proposed, including envy-freeness, Pareto optimality, and maximization of either the total welfare of all agents, the welfare of the worst-off agent, or the Nash product of agents’ welfares. In the two-person context, we study relationships among these properties using both analytical models and simulation in a setting where individual preferences are given by additive cardinal utilities. We provide several new theorems linking these criteria and use simulation to study how their values are related to problem characteristics, assuming that utilities are assigned randomly. We draw some conclusions concerning the relation of problem characteristics to the availabilty of allocations with particular properties.

Suggested Citation

  • D. Marc Kilgour & Rudolf Vetschera, 2024. "Two-Person Fair Division with Additive Valuations," Group Decision and Negotiation, Springer, vol. 33(4), pages 745-774, August.
    • Handle: RePEc:spr:grdene:v:33:y:2024:i:4:d:10.1007_s10726-024-09885-x
    DOI: 10.1007/s10726-024-09885-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10726-024-09885-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10726-024-09885-x?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. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    2. Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2017. "Maximin Envy-Free Division of Indivisible Items," Group Decision and Negotiation, Springer, vol. 26(1), pages 115-131, January.
    3. Yuen, Sheung Man & Suksompong, Warut, 2023. "Extending the characterization of maximum Nash welfare," Economics Letters, Elsevier, vol. 224(C).
    4. Butler, John & Jia, Jianmin & Dyer, James, 1997. "Simulation techniques for the sensitivity analysis of multi-criteria decision models," European Journal of Operational Research, Elsevier, vol. 103(3), pages 531-546, December.
    5. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
    6. Suksompong, Warut, 2023. "A characterization of maximum Nash welfare for indivisible goods," Economics Letters, Elsevier, vol. 222(C).
    7. Shiran Rachmilevitch, 2015. "The Nash solution is more utilitarian than egalitarian," Theory and Decision, Springer, vol. 79(3), pages 463-478, November.
    8. 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. Suksompong, Warut & Teh, Nicholas, 2023. "Weighted fair division with matroid-rank valuations: Monotonicity and strategyproofness," Mathematical Social Sciences, Elsevier, vol. 126(C), pages 48-59.
    2. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Coordinating Charitable Donations," Papers 2305.10286, arXiv.org, revised Sep 2024.
    3. Warut Suksompong & Nicholas Teh, 2023. "Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness," Papers 2303.14454, arXiv.org, revised Sep 2023.
    4. Andreas Darmann & Christian Klamler, 2019. "Using the Borda rule for ranking sets of objects," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(3), pages 399-414, October.
    5. Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2022. "Two-Person Fair Division of Indivisible Items when Envy-Freeness is Impossible," SN Operations Research Forum, Springer, vol. 3(2), pages 1-23, June.
    6. Yuen, Sheung Man & Suksompong, Warut, 2023. "Extending the characterization of maximum Nash welfare," Economics Letters, Elsevier, vol. 224(C).
    7. Carmen Beviá, 2010. "Manipulation games in economies with indivisible goods," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 209-222, March.
    8. Wang, Xianjia & Lv, Shaojie, 2019. "The roles of particle swarm intelligence in the prisoner’s dilemma based on continuous and mixed strategy systems on scale-free networks," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 213-220.
    9. Mohammed A. Al-Ghamdi & Khalid S. Al-Gahtani, 2022. "Integrated Value Engineering and Life Cycle Cost Modeling for HVAC System Selection," Sustainability, MDPI, vol. 14(4), pages 1-30, February.
    10. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    11. Rodrigo A. Velez, 2020. "A polynomial algorithm for maxmin and minmax envy-free rent division on a soft budget," Papers 2002.02966, arXiv.org.
    12. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    13. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    14. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    15. Nicolò, Antonio & Yu, Yan, 2008. "Strategic divide and choose," Games and Economic Behavior, Elsevier, vol. 64(1), pages 268-289, September.
    16. Velez, Rodrigo A., 2011. "Are incentives against economic justice?," Journal of Economic Theory, Elsevier, vol. 146(1), pages 326-345, January.
    17. Hervé Moulin, 2010. "Auctioning or assigning an object: some remarkable VCG mechanisms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(2), pages 193-216, February.
    18. Shinji Ohseto, 2006. "Characterizations of strategy-proof and fair mechanisms for allocating indivisible goods," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 111-121, September.
    19. Dolgopolov, Arthur & Houser, Daniel & Martinelli, Cesar & Stratmann, Thomas, 2024. "Assignment markets: Theory and experiments," European Economic Review, Elsevier, vol. 165(C).
    20. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.

    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:spr:grdene:v:33:y:2024:i:4:d:10.1007_s10726-024-09885-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.