IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2209.06437.html
   My bibliography  Save this paper

Weighted Envy-Freeness for Submodular Valuations

Author

Listed:
  • Luisa Montanari
  • Ulrike Schmidt-Kraepelin
  • Warut Suksompong
  • Nicholas Teh

Abstract

We investigate the fair allocation of indivisible goods to agents with possibly different entitlements represented by weights. Previous work has shown that guarantees for additive valuations with existing envy-based notions cannot be extended to the case where agents have matroid-rank (i.e., binary submodular) valuations. We propose two families of envy-based notions for matroid-rank and general submodular valuations, one based on the idea of transferability and the other on marginal values. We show that our notions can be satisfied via generalizations of rules such as picking sequences and maximum weighted Nash welfare. In addition, we introduce welfare measures based on harmonic numbers, and show that variants of maximum weighted harmonic welfare offer stronger fairness guarantees than maximum weighted Nash welfare under matroid-rank valuations.

Suggested Citation

  • Luisa Montanari & Ulrike Schmidt-Kraepelin & Warut Suksompong & Nicholas Teh, 2022. "Weighted Envy-Freeness for Submodular Valuations," Papers 2209.06437, arXiv.org.
    • Handle: RePEc:arx:papers:2209.06437
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2209.06437
    File Function: Latest version
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Warut Suksompong & Nicholas Teh, 2023. "Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness," Papers 2303.14454, arXiv.org, revised Sep 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2209.06437. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.