{"type":"ScholarlyArticle","title":"Computational Aspects of Equilibria in Discrete Preference Games","authors":[{"name":"Phani Raj Lolakapuri","slug":"phani-raj-lolakapuri","given":"Phani Raj","family":"Lolakapuri","affiliation":"TIFR Mumbai , India"},{"name":"Umang Bhaskar","slug":"umang-bhaskar","given":"Umang","family":"Bhaskar","affiliation":"TIFR Mumbai , India"},{"name":"Ramasuri Narayanam","slug":"ramasuri-narayanam","given":"Ramasuri","family":"Narayanam","affiliation":"IBM Research , India"},{"name":"Gyana R Parija","slug":"gyana-r-parija","given":"Gyana R","family":"Parija","affiliation":"IBM Research , India"},{"name":"Pankaj S Dayama","slug":"pankaj-s-dayama","given":"Pankaj S","family":"Dayama","affiliation":"IBM Research , India"}],"abstract":"We study the complexity of equilibrium computation in discrete preference games. These games were introduced by Chierichetti, Kleinberg, and Oren (EC '13, JCSS '18) to model decision-making by agents in a social network that choose a strategy from a finite, discrete set, balancing between their intrinsic preferences for the strategies and their desire to choose a strategy that is `similar' to their neighbours. There are thus two components: a social network with the agents as vertices, and a metric space of strategies. These games are potential games, and hence pure Nash equilibria exist. Since their introduction, a number of papers have studied various aspects of this model, including the social cost at equilibria, and arrival at a consensus. We show that in general, equilibrium computation in discrete preference games is PLS-complete, even in the simple case where each agent has a constant number of neighbours. If the edges in the social network are weighted, then the problem is PLS-complete even if each agent has a constant number of neighbours, the metric space has constant size, and every pair of strategies is at distance 1 or 2. Further, if the social network is directed, modelling asymmetric influence, an equilibrium may not even exist. On the positive side, we show that if the metric space is a tree metric, or is the product of path metrics, then the equilibrium can be computed in polynomial time.","doi":"10.24963/ijcai.2019/67","url":"https://ijcai.org/proceedings/2019/67","pdf":"https://ijcai.org/proceedings/2019/0067.pdf","markdown":"https://ijcai.org/proceedings/2019/67.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/67","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":67,"pages":{"first":471,"last":477},"keywords":["Agent-based and Multi-agent Systems: Noncooperative Games","Agent-based and Multi-agent Systems: Algorithmic Game Theory"],"videos":[],"references":[{"position":1,"raw":"[Acemoglu et al., 2011] Daron Acemoglu, Munther A Dahleh, Ilan Lobel, and Asuman Ozdaglar. 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