Pith. sign in

REVIEW 1 cited by

Fair allocations with subadditive and XOS valuations

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2503.10513 v1 pith:FLQYA2IJ submitted 2025-03-13 cs.GT

classification cs.GT
keywords caseallocationsfracsubadditiveentitlementresultsvaluationsarbitrary
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We consider the problem of fair allocation of $m$ indivisible goods to $n$ agents with either subadditive or XOS valuations, in the arbitrary entitlement case. As fairness notions, we consider the anyprice share (APS) ex-post, and the maximum expectation share (MES) ex-ante. We observe that there are randomized allocations that ex-ante are at least $\frac{1}{2}$-MES in the subadditive case and $(1-\frac{1}{e})$-MES in the XOS case. Our more difficult results concern ex-post guarantees. We show that $(1 - o(1))\frac{\log\log m}{\log m}$-APS allocations exist in the subadditive case, and $\frac{1}{6}$-APS allocations exist in the XOS case. For the special case of equal entitlements, we show $\frac{4}{17}$-APS allocations for XOS. Our results are the first for subadditive and XOS valuations in the arbitrary entitlement case, and also improve over the previous best results for the equal entitlement case.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. From multi-allocations to allocations, with subadditive valuations

    cs.GT 2025-06 conditional novelty 7.0 of 10

    A d-multi-allocation with subadditive valuations can be converted to an allocation losing only a factor of about d, yielding an Omega(1/log log n)-MMS guarantee.

Pith tools