{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:46:29Z","timestamp":1759063589112},"reference-count":0,"publisher":"Association for the Advancement of Artificial Intelligence (AAAI)","issue":"01","license":[{"start":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T00:00:00Z","timestamp":1563321600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.aaai.org"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AAAI"],"abstract":"<jats:p>We consider a fair division setting in which m indivisible items are to be allocated among n agents, where the agents have additive utilities and the agents\u2019 utilities for individual items are independently sampled from a distribution. Previous work has shown that an envy-free allocation is likely to exist when m = \u2126 (n log n) but not when m = n + o (n), and left open the question of determining where the phase transition from non-existence to existence occurs. We show that, surprisingly, there is in fact no universal point of transition\u2014 instead, the transition is governed by the divisibility relation between m and n. On the one hand, if m is divisible by n, an envy-free allocation exists with high probability as long as m \u2265 2n. On the other hand, if m is not \u201calmost\u201d divisible by , an envy-free allocation is unlikely to exist even when m = \u0398(n log n)\/log log n).<\/jats:p>","DOI":"10.1609\/aaai.v33i01.33012109","type":"journal-article","created":{"date-parts":[[2019,9,10]],"date-time":"2019-09-10T07:49:28Z","timestamp":1568101768000},"page":"2109-2116","source":"Crossref","is-referenced-by-count":3,"title":["When Do Envy-Free Allocations Exist?"],"prefix":"10.1609","volume":"33","author":[{"given":"Pasin","family":"Manurangsi","sequence":"first","affiliation":[]},{"given":"Warut","family":"Suksompong","sequence":"additional","affiliation":[]}],"member":"9382","published-online":{"date-parts":[[2019,7,17]]},"container-title":["Proceedings of the AAAI Conference on Artificial Intelligence"],"original-title":[],"link":[{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/4042\/3920","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/download\/4042\/3920","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,7]],"date-time":"2022-11-07T06:29:21Z","timestamp":1667802561000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/4042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,17]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,7,23]]}},"URL":"https:\/\/doi.org\/10.1609\/aaai.v33i01.33012109","relation":{},"ISSN":["2374-3468","2159-5399"],"issn-type":[{"value":"2374-3468","type":"electronic"},{"value":"2159-5399","type":"print"}],"subject":[],"published":{"date-parts":[[2019,7,17]]}}}