{"paper":{"title":"EFX Exists for Three Types of Agents","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DS","cs.MA"],"primary_cat":"cs.GT","authors_text":"Nithin Varma, Prajakta Nimbhorkar, Pratik Ghosal, Vishwa Prakash HV","submitted_at":"2024-10-17T14:15:08Z","abstract_excerpt":"We study the problem of finding an envy-free allocation of indivisible goods among agents with additive valuations. We focus on the fairness notion of envy-freeness up to any good (EFX). A central open question in fair division is whether EFX allocations always exist for any number of agents. While EFX has been established for three agents [CGM24] and for any number of agents with at most two distinct valuations [Mah23], its existence in more general settings remains open.\n  In this paper, we make significant progress by proving that EFX allocations exist for any number of agents when there ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13580","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.13580/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}