{"type":"ScholarlyArticle","title":"Complexity of Efficient Outcomes in Binary-Action Polymatrix Games and Implications for Coordination Problems","authors":[{"name":"Argyrios Deligkas","slug":"argyrios-deligkas","given":"Argyrios","family":"Deligkas","affiliation":"Royal Holloway , University of London"},{"name":"Eduard Eiben","slug":"eduard-eiben","given":"Eduard","family":"Eiben","affiliation":"Royal Holloway , University of London"},{"name":"Gregory Gutin","slug":"gregory-gutin","given":"Gregory","family":"Gutin","affiliation":"Royal Holloway , University of London"},{"name":"Philip Neary","slug":"philip-neary","given":"Philip","family":"Neary","affiliation":"Royal Holloway , University of London"},{"name":"Anders Yeo","slug":"anders-yeo","given":"Anders","family":"Yeo","affiliation":"University of Southern Denmark; University of Johannesburg"}],"abstract":"We investigate the difficulty of finding economically efficient solutions to coordination problems on graphs. Our work focuses on two forms of coordination problem: pure-coordination games and anti-coordination games. We consider three objectives in the context of simple binary-action polymatrix games: (i) maximizing welfare, (ii) maximizing potential, and (iii) finding a welfare-maximizing Nash equilibrium. We introduce an intermediate, new graph-partition problem, termed MWDP, which is of independent interest, and we provide a  complexity dichotomy for it. This dichotomy, among other results, provides as a corollary a dichotomy for Objective (i) for general binary-action polymatrix games. In addition, it reveals that the complexity of achieving these objectives varies depending on the form of the coordination problem. Specifically, Objectives (i) and (ii) can be efficiently solved in pure-coordination games, but are NP-hard in anti-coordination games. Finally, we show that objective (iii) is NP-hard even for simple non-trivial pure-coordination games.","doi":"10.24963/ijcai.2023/294","url":"https://ijcai.org/proceedings/2023/294","pdf":"https://ijcai.org/proceedings/2023/0294.pdf","markdown":"https://ijcai.org/proceedings/2023/294.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/294","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":294,"pages":{"first":2642,"last":2650},"keywords":["Agent-based and Multi-agent Systems: MAS: Coordination and cooperation","Game Theory and Economic Paradigms: GTEP: Noncooperative games"],"videos":[],"references":[{"position":1,"raw":"[Aloisio et al., 2021] Alessandro Aloisio, Michele Flam- mini, Bojana Kodric, and Cosimo Vinci. 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