Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fairly Dividing Mixtures of Goods and Chores under Lexicographic
  Preferences   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.

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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th