{"paper":{"title":"Tight Guarantees in the Commons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT"],"primary_cat":"econ.TH","authors_text":"Anna Bogomolnaia, Herv\\'e Moulin","submitted_at":"2024-06-20T11:03:51Z","abstract_excerpt":"In our context-free model of a commons, the function$\\mathcal{W}$ transforms the profile of the agents' types $(x_{1},..,x_{n})$ to a freely transferable output $\\mathcal{W}(x_{1},..,x_{n})$ that they must share fairly. We expand the ubiquitous concept of \\textit{endogenous fair shares} to include both a lower and an upper bound on agent $i$'s share at the interim stage where $i$ only knows its own type $x_{i}$. Two functions $(g^{-},g^{+})$ form a pair of tight guarantees if 1) they satisfy the system of inequalities $% \\sum_{1}^{n}g^{-}(x_{i})\\leq \\mathcal{W}(x)\\leq \\sum_{1}^{n}g^{+}(x_{i})$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.14198","kind":"arxiv","version":4},"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/2406.14198/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"}