{"type":"ScholarlyArticle","title":"How to Resolve Envy by Adding Goods","authors":[{"name":"Matthias Bentert","slug":"matthias-bentert","given":"Matthias","family":"Bentert","affiliation":""},{"name":"Robert Bredereck","slug":"robert-bredereck","given":"Robert","family":"Bredereck","affiliation":""},{"name":"Eva Deltl","slug":"eva-deltl","given":"Eva","family":"Deltl","affiliation":""},{"name":"Pallavi Jain","slug":"pallavi-jain","given":"Pallavi","family":"Jain","affiliation":""},{"name":"Leon Kellerhals","slug":"leon-kellerhals","given":"Leon","family":"Kellerhals","affiliation":""}],"abstract":"We consider the problem of resolving the envy of a given initial allocation by adding elements from a pool of goods. We give a characterization of the instances where envy can be resolved by adding an arbitrary number of copies of the items in the pool. From this characterization, we derive a polynomial-time algorithm returning a respective solution if it exists. If the number of copies or the total number of added items are bounded, the problem becomes computationally intractable even in various restricted cases. We perform a parameterized complexity analysis, focusing on the number of agents and the pool size as parameters. Notably, although not every instance admits an envy-free solution, our approach allows us to efficiently determine, in polynomial time, whether a solution exists—an aspect that is both theoretically interesting and far from trivial.","doi":"10.24963/ijcai.2025/417","url":"https://ijcai.org/proceedings/2025/417","pdf":"https://ijcai.org/proceedings/2025/0417.pdf","markdown":"https://ijcai.org/proceedings/2025/417.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/417","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":417,"pages":{"first":3753,"last":3761},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}