{"type":"ScholarlyArticle","title":"Non-Obvious Manipulability in Additively Separable and Fractional Hedonic Games","authors":[{"name":"Diodato Ferraioli","slug":"diodato-ferraioli","given":"Diodato","family":"Ferraioli","affiliation":""},{"name":"Giovanna Varricchio","slug":"giovanna-varricchio","given":"Giovanna","family":"Varricchio","affiliation":""}],"abstract":"In this work, we consider the design of Non-Obviously Manipulable (NOM) mechanisms, mechanisms that bounded rational agents may fail to recognize as manipulable, for two relevant classes of succinctly representable Hedonic Games: Additively Separable and Fractional Hedonic Games. In these classes, agents have cardinal scores towards other agents, and their preferences over coalitions are determined by aggregating such scores. \r\nThis aggregation results in a utility function for each agent, which enables the evaluation of outcomes via the utilitarian social welfare.\r\nWe first prove that, when scores can be arbitrary, every optimal mechanism is NOM; moreover, when scores are limited in a continuous interval, an optimal mechanism that is NOM exists.\r\nGiven the hardness of computing optimal outcomes in these settings, we turn our attention to efficient and NOM mechanisms. To this aim, we first prove a characterization of NOM mechanisms that simplifies the class of mechanisms of interest. Then, we design a NOM mechanism returning approximations that asymptotically match the best-known approximation achievable in polynomial time.\r\nFinally, we focus on discrete scores, where the compatibility of NOM with optimality depends on the specific values. \r\nTherefore, we initiate a systematic analysis to identify which discrete values support this compatibility and which do not.","doi":"10.24963/ijcai.2025/428","url":"https://ijcai.org/proceedings/2025/428","pdf":"https://ijcai.org/proceedings/2025/0428.pdf","markdown":"https://ijcai.org/proceedings/2025/428.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/428","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":428,"pages":{"first":3848,"last":3856},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Mechanism design","Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}