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. Shiran Rachmilevitch, 2015. "The Nash solution is more utilitarian than egalitarian," Theory and Decision, Springer, vol. 79(3), pages 463-478, November.
    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. 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.
    4. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    5. Yuen, Sheung Man & Suksompong, Warut, 2023. "Extending the characterization of maximum Nash welfare," Economics Letters, Elsevier, vol. 224(C).
    6. Suksompong, Warut, 2023. "A characterization of maximum Nash welfare for indivisible goods," Economics Letters, Elsevier, vol. 222(C).
    7. 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.
    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. Warut Suksompong & Nicholas Teh, 2023. "Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness," Papers 2303.14454, arXiv.org, revised Sep 2023.
    3. Felix Brandt & Matthias Greger & Erel Segal-Halevi & Warut Suksompong, 2023. "Coordinating Charitable Donations," Papers 2305.10286, arXiv.org, revised Sep 2024.
    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. 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.
    8. Sheung Man Yuen & Warut Suksompong, 2023. "Extending the Characterization of Maximum Nash Welfare," Papers 2301.03798, arXiv.org, revised Feb 2023.
    9. 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.
    10. 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.
    11. 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.
    12. Tsuyoshi Adachi & Takumi Kongo, 2013. "First-price auctions on general preference domains: axiomatic characterizations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 93-103, May.
    13. Borgonovo, E., 2010. "Sensitivity analysis with finite changes: An application to modified EOQ models," European Journal of Operational Research, Elsevier, vol. 200(1), pages 127-138, January.
    14. Marco Grasso, 2004. "A Normative Framework of Justice in Climate Change," Working Papers 79, University of Milano-Bicocca, Department of Economics, revised Jul 2004.
    15. , & ,, 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.
    16. Mustajoki, Jyri & Hamalainen, Raimo P. & Lindstedt, Mats R.K., 2006. "Using intervals for global sensitivity and worst-case analyses in multiattribute value trees," European Journal of Operational Research, Elsevier, vol. 174(1), pages 278-292, October.
    17. McKenna, R. & Bertsch, V. & Mainzer, K. & Fichtner, W., 2018. "Combining local preferences with multi-criteria decision analysis and linear optimization to develop feasible energy concepts in small communities," European Journal of Operational Research, Elsevier, vol. 268(3), pages 1092-1110.
    18. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2014. "Egalitarian equivalence and strategyproofness in the queueing problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 425-442, June.
    19. Meertens, Marc & Potters, Jos & Reijnierse, Hans, 2002. "Envy-free and Pareto efficient allocations in economies with indivisible goods and money," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 223-233, December.
    20. Klijn, Flip & Tijs, Stef & Hamers, Herbert, 2000. "Balancedness of permutation games and envy-free allocations in indivisible good economies," Economics Letters, Elsevier, vol. 69(3), pages 323-326, December.

    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.