Fairly Dividing Mixtures of Goods and Chores under Lexicographic Preferences

Hadi Hosseini, Sujoy Sikdar, Rohit Vaish and Lirong Xia

Papers from arXiv.org

Abstract: We study fair allocation of indivisible goods and chores among agents with \emph{lexicographic} preferences -- a subclass of additive valuations. In sharp contrast to the goods-only setting, we show that an allocation satisfying \emph{envy-freeness up to any item} (EFX) could fail to exist for a mixture of \emph{objective} goods and chores. To our knowledge, this negative result provides the \emph{first} counterexample for EFX over (any subdomain of) additive valuations. To complement this non-existence result, we identify a class of instances with (possibly subjective) mixed items where an EFX and Pareto optimal allocation always exists and can be efficiently computed. When the fairness requirement is relaxed to \emph{maximin share} (MMS), we show positive existence and computation for \emph{any} mixed instance. More broadly, our work examines the existence and computation of fair and efficient allocations both for mixed items as well as chores-only instances, and highlights the additional difficulty of these problems vis-{\`a}-vis their goods-only counterparts.

Date: 2022-03
New Economics Papers: this item is included in nep-des and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2203.07279 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2203.07279

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().