{"type":"ScholarlyArticle","title":"When Does Schwartz Conjecture Hold?","authors":[{"name":"Matthias Mnich","slug":"matthias-mnich","given":"Matthias","family":"Mnich","affiliation":""},{"name":"Yash Raj Shrestha","slug":"yash-raj-shrestha","given":"Yash Raj","family":"Shrestha","affiliation":""},{"name":"Yongjie Yang","slug":"yongjie-yang","given":"Yongjie","family":"Yang","affiliation":""}],"abstract":"In 1990, Thomas Schwartz proposed the conjecture that every nonempty tournament has a unique minimal TEQ-retentive set (TEQ stands for tournament equilibrium set). A weak variant of Schwartz's Conjecture was recently proposed by Felix Brandt. However, both conjectures were disproved very recently by two counterexamples. In this paper, we prove sufficient conditions for infinite classes of tournaments that satisfy Schwartz's Conjecture and Brandt's Conjecture. Moreover, we prove that TEQ can be calculated in polynomial time in several infinite classes of tournaments. Furthermore, our results reveal some structures that are forbidden in every counterexample to Schwartz's Conjecture.","doi":null,"url":"https://ijcai.org/proceedings/2015/91","pdf":"https://ijcai.org/proceedings/2015/0091.pdf","markdown":"https://ijcai.org/proceedings/2015/91.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/91","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Game Theory","track":"Main Track","number":91,"pages":{"first":603,"last":608},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}