{"type":"ScholarlyArticle","title":"Possibilistic Games with Incomplete Information","authors":[{"name":"Nahla Ben Amor","slug":"nahla-ben-amor","given":"Nahla Ben","family":"Amor","affiliation":"ISG-Tunis , Université de Tunis"},{"name":"Helene Fargier","slug":"helene-fargier","given":"Helene","family":"Fargier","affiliation":"IRIT-CNRS , Université de Toulouse"},{"name":"Régis Sabbadin","slug":"regis-sabbadin","given":"Régis","family":"Sabbadin","affiliation":"INRA-MIAT , Université de Toulouse"},{"name":"Meriem Trabelsi","slug":"meriem-trabelsi","given":"Meriem","family":"Trabelsi","affiliation":"ISG-Tunis , Université de Tunis; IRIT-CNRS , Université de Toulouse"}],"abstract":"Bayesian games offer a suitable framework for\r\ngames where the utility degrees are additive in\r\nessence. This approach does nevertheless not apply to ordinal games, where the utility degrees do\r\nnot capture more than a ranking, nor to situations\r\nof decision under qualitative uncertainty. This paper proposes a representation framework for ordinal games under possibilistic incomplete information (π-games) and extends the fundamental notion\r\nof Nash equilibrium (NE) to this framework. We\r\nshow that deciding whether a NE exists is a difficult\r\nproblem (NP-hard) and propose a  Mixed Integer Linear Programming  (MILP) encoding.\r\nExperiments on variants of the GAMUT problems\r\nconfirm the feasibility of this approach.","doi":"10.24963/ijcai.2019/214","url":"https://ijcai.org/proceedings/2019/214","pdf":"https://ijcai.org/proceedings/2019/0214.pdf","markdown":"https://ijcai.org/proceedings/2019/214.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/214","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":"Knowledge Representation and Reasoning","track":"Main track","number":214,"pages":{"first":1544,"last":1550},"keywords":["Agent-based and Multi-agent Systems: Noncooperative Games","Agent-based and Multi-agent Systems: Algorithmic Game Theory","Knowledge Representation and Reasoning: Knowledge Representation and  Game Theory ; Social Choice","Uncertainty in AI: Uncertainty in AI","Uncertainty in AI: Nonprobabilistic Models","Knowledge Representation and Reasoning: Qualitative Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Battigalli and Bonanno, 1999] Pierpaolo Battigalli and Gia- como Bonanno. 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