{"type":"ScholarlyArticle","title":"Winning a Tournament by Any Means Necessary","authors":[{"name":"Sushmita Gupta","slug":"sushmita-gupta","given":"Sushmita","family":"Gupta","affiliation":"University of Bergen , Bergen , Norway"},{"name":"Sanjukta Roy","slug":"sanjukta-roy","given":"Sanjukta","family":"Roy","affiliation":"The Institute of Mathematical Sciences , HBNI , Chennai , India"},{"name":"Saket Saurabh","slug":"saket-saurabh","given":"Saket","family":"Saurabh","affiliation":"University of Bergen , Bergen , Norway"},{"name":"Meirav Zehavi","slug":"meirav-zehavi","given":"Meirav","family":"Zehavi","affiliation":"The Institute of Mathematical Sciences , HBNI , Chennai , India; Ben-Gurion University , Beersheba , Israel"}],"abstract":"In a tournament, $n$ players enter the competition. In each round, they are paired-up to compete against each other. Losers are thrown, while winners proceed to the next round, until only one player (the winner) is left. Given a prediction of the outcome, for every pair of players, of a match between them (modeled by a digraph $D$), the competitive nature of a tournament makes it attractive for manipulators. In the Tournament Fixing (TF) problem, the goal is to decide if we can conduct the competition (by controlling how players are paired-up) so that our favorite player $w$ wins. A common form of manipulation is to bribe players to alter the outcome of matches. Kim and Williams [IJCAI 2015] integrated such deceit into TF, and showed that the resulting problem is NP-hard when $\\ell<(1-\\epsilon)\\log n$ alterations are possible (for any fixed $\\epsilon>0$). For this problem, our contribution is fourfold. First, we present two operations  that ``obfuscate deceit'': given one solution, they produce another solution. Second, we present a combinatorial result, stating that there is always a solution with all reversals incident to $w$ and ``elite players''. Third, we give a closed formula for the case where $D$ is a DAG. Finally, we present exact exponential-time and parameterized algorithms for the general case.","doi":"10.24963/ijcai.2018/39","url":"https://ijcai.org/proceedings/2018/39","pdf":"https://ijcai.org/proceedings/2018/0039.pdf","markdown":"https://ijcai.org/proceedings/2018/39.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/39","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":39,"pages":{"first":282,"last":288},"keywords":["Agent-based and Multi-agent Systems: Voting","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[],"references":[{"position":1,"raw":"[Amini et al., 2012] Omid Amini, Fedor V. 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