{"type":"ScholarlyArticle","title":"The Tractability of the Shapley Value over Bounded Treewidth Matching Games","authors":[{"name":"Gianluigi Greco","slug":"gianluigi-greco","given":"Gianluigi","family":"Greco","affiliation":"University of Calabria , Italy"},{"name":"Francesco Lupia","slug":"francesco-lupia","given":"Francesco","family":"Lupia","affiliation":"University of Calabria , Italy"},{"name":"Francesco Scarcello","slug":"francesco-scarcello","given":"Francesco","family":"Scarcello","affiliation":"University of Calabria , Italy"}],"abstract":"Matching games form a class of coalitional games that attracted much attention in the literature. Indeed, several results are known about the complexity of computing over them {solution concepts}. In particular, it is known that computing the Shapley value is intractable in general, formally #P-hard, and feasible in polynomial time over games defined on trees. In fact, it was an open problem whether or not this tractability result holds over classes of graphs properly including acyclic ones. The main contribution of the paper is to provide a positive answer to this question, by showing that the Shapley value is tractable for matching games defined over graphs having bounded treewidth. The proposed technique has been implemented and tested on classes of graphs having different sizes and treewidth at most three.","doi":"10.24963/ijcai.2017/145","url":"https://ijcai.org/proceedings/2017/145","pdf":"https://ijcai.org/proceedings/2017/0145.pdf","markdown":"https://ijcai.org/proceedings/2017/145.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/145","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Knowledge Representation, Reasoning, and Logic","track":"Main track","number":145,"pages":{"first":1046,"last":1052},"keywords":["Agent-based and Multi-agent Systems: Cooperative Games","Combinatorial & Heuristic Search: Combinatorial search/optimisation","Knowledge Representation, Reasoning, and Logic: Game Theory"],"videos":[],"references":[{"position":1,"raw":"[Alkan and Gale, 1990] Ahmet Alkan and David Gale. 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