{"type":"ScholarlyArticle","title":"Asymptotic Analysis of Weighted Fair Division","authors":[{"name":"Pasin Manurangsi","slug":"pasin-manurangsi","given":"Pasin","family":"Manurangsi","affiliation":""},{"name":"Warut Suksompong","slug":"warut-suksompong","given":"Warut","family":"Suksompong","affiliation":""},{"name":"Tomohiko Yokoyama","slug":"tomohiko-yokoyama","given":"Tomohiko","family":"Yokoyama","affiliation":""}],"abstract":"Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if m items are divided among n agents whose utilities are independently sampled from a probability distribution, when is it likely that a fair allocation exist? We show that if the ratio between the weights is bounded, a weighted envy-free allocation exists with high probability provided that m = Omega(n log n / log log n), generalizing a prior unweighted result. For weighted proportionality, we establish a sharp threshold of m = n / (1 - \\mu) for the transition from non-existence to existence, where \\mu in (0,1) denotes the mean of the distribution. In addition, we prove that for two agents, a weighted envy-free (and weighted proportional) allocation is likely to exist if m = omega(sqrt{r}), where r denotes the ratio between the two weights.","doi":"10.24963/ijcai.2025/443","url":"https://ijcai.org/proceedings/2025/443","pdf":"https://ijcai.org/proceedings/2025/0443.pdf","markdown":"https://ijcai.org/proceedings/2025/443.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/443","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":443,"pages":{"first":3979,"last":3987},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division","Agent-based and Multi-agent Systems: MAS: Resource allocation"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}