{"type":"ScholarlyArticle","title":"Equilibria in Ordinal Games: A Framework based on Possibility Theory.","authors":[{"name":"Nahla Ben Amor","slug":"nahla-ben-amor","given":"Nahla Ben","family":"Amor","affiliation":"ISG-Tunis"},{"name":"Helene Fargier","slug":"helene-fargier","given":"Helene","family":"Fargier","affiliation":"Université de Toulouse"},{"name":"Régis Sabbadin","slug":"regis-sabbadin","given":"Régis","family":"Sabbadin","affiliation":"INRA-MIAT , Université de Toulouse"}],"abstract":"The present paper proposes the first definition of mixed equilibrium for ordinal games. This definition naturally extends possibilistic (single agent) decision theory. This allows us to provide a unifying view of single and multi-agent qualitative decision theory. Our first contribution is to show that ordinal games always admit a possibilistic mixed equilibrium, which can be seen as a qualitative counterpart to mixed (probabilistic) equilibrium.Then, we show that a possibilistic mixed equilibrium can be computed in polynomial time (wrt the size of the game), which contrasts with pure Nash or mixed probabilistic equilibrium computation in cardinal game theory.The definition we propose is thus operational in two ways: (i) it tackles the case when no pure Nash equilibrium exists in an ordinal game; and (ii) it allows an efficient computation of a mixed equilibrium.","doi":"10.24963/ijcai.2017/16","url":"https://ijcai.org/proceedings/2017/16","pdf":"https://ijcai.org/proceedings/2017/0016.pdf","markdown":"https://ijcai.org/proceedings/2017/16.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/16","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":16,"pages":{"first":105,"last":111},"keywords":["Uncertainty in AI: Uncertainty in AI","Agent-based and Multi-agent Systems: Noncooperative Games"],"videos":[],"references":[{"position":1,"raw":"[Barany et al., 1992] Imre Barany, Jon Lee, and Martin Shu- bik. Classification of two-person ordinal bimatrix games. International Journal of Game Theory, 21:267-290, 1992.","title":"Classification of two-person ordinal bimatrix games","authors":"Barany","year":"1992","venue":"International Journal of Game Theory","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Cassandra et al., 1994] Anthony R. Cassandra, Leslie Pack Kaelbling, and Michael L. Littman. Acting optimally in partially observable stochastic domains. In Proceedings of the 12th National Conference on Artificial Intelligence (AAAI'94), pages 1023-1028, 1994.","title":"Acting optimally in partially observable stochastic domains","authors":"Anthony R Cassandra, Leslie Pack Kaelbling, Michael L Littman","year":"1994","venue":"Proceedings of the 12th National Conference on Artificial Intelligence (AAAI'94)","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Cruz Jr. and Simaan, 2000] Jose B. Cruz Jr. and Marwan A. Simaan. Ordinal games and generalized nash and stackel- berg solutions. Journal of Optimization Theory and Appli- cations, 107:205-222, 2000.","title":"Ordinal games and generalized nash and stackelberg solutions","authors":"Jose B Cruz, A Marwan, Simaan","year":"2000","venue":"Journal of Optimization Theory and Applications","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Daskalakis et al., 2006] Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou. The complex- ity of computing a Nash equilibrium. In Proceedings of the 38th Annual ACM Symposium on Theory of Comput- ing, pages 71-78, 2006.","title":"The complexity of computing a Nash equilibrium","authors":"Constantinos Daskalakis, Paul W Goldberg, Christos H Papadimitriou","year":"2006","venue":"Proceedings of the 38th Annual ACM Symposium on Theory of Computing","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[De Clercq et al., 2014] Sofie De Clercq, Steven Schockaert, Martin De Cock, and Ann Nowé. Possibilistic boolean games: Strategic reasoning under incomplete information. In Proceedings of the 14th European conference on Log- ics in Artificial Intelligence (JELIA 2014), pages 196-209, 2014.","title":"Possibilistic boolean games: Strategic reasoning under incomplete information","authors":"De Clercq","year":"2014","venue":"Proceedings of the 14th European conference on Logics in Artificial Intelligence (JELIA 2014)","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[De Clercq et al., 2015] Sofie De Clercq, Steven Schockaert, Ann Nowé, and Martin De Cock. Multilateral negotiation in boolean games with incomplete information using gen- eralized possibilistic logic. In Proceedings of the Inter- national Joint Conference on Artificial Intelligence (IJCAI 2015), pages 2890-2896, 2015.","title":"Multilateral negotiation in boolean games with incomplete information using generalized possibilistic logic","authors":"De Clercq","year":"2015","venue":"Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI 2015)","doi":null,"url":null,"internal_url":"/proceedings/2015/409"},{"position":7,"raw":"[Dubois and Prade, 1988] Didier Dubois and Henri Prade. Possibility Theory. Plenum Press, New York, 1988.","title":"Possibility Theory","authors":"Didier Dubois, Henri Prade","year":"1988","venue":null,"doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dubois and Prade, 1995] Didier Dubois and Henri Prade. Possibility theory as a basis for qualitative decision the- ory. In Proceedings of the 14th international joint con- ference on Artificial intelligence (IJCAI'95), pages 1925- 1930, 1995.","title":"Possibility theory as a basis for qualitative decision theory","authors":"Prade Dubois, Didier Dubois, Henri Prade","year":"1995","venue":"Proceedings of the 14th international joint conference on Artificial intelligence (IJCAI'95)","doi":null,"url":null,"internal_url":"/proceedings/1995/247"},{"position":9,"raw":"[Dubois et al., 2001] Didier Dubois, Henri Prade, and Régis Sabbadin. Decision-theoretic foundations of qualitative possibility theory. European Journal of Operational Re- search, 128:459-478, 2001.","title":"Decision-theoretic foundations of qualitative possibility theory","authors":"Didier Dubois, Henri Prade, Régis Sabbadin","year":"2001","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Durieu et al., 2008] Jacques Durieu, Hans Haller, Nicolas Quérou, and Philippe Solal. Ordinal games. International Game Theory Review, 10(2):177-194, 2008.","title":"Ordinal games","authors":"Jacques Durieu, Hans Haller, Nicolas Quérou, Philippe Solal","year":"2008","venue":"International Game Theory Review","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Filar and Vrieze, 1997] Jerzy Filar and Koos Vrieze. Com- petitive Markov Decision Processes. Springer, 1997.","title":"Competitive Markov Decision Processes","authors":"Vrieze Filar, Jerzy Filar, Koos Vrieze","year":"1997","venue":null,"doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Harsanyi, 1967] John C. Harsanyi. Games with incomplete information played by \"Bayesian\" players. Management Science, 14:159-182, 1967.","title":"Games with incomplete information played by \"Bayesian\" players","authors":"John C Harsanyi","year":"1967","venue":"Management Science","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Monderer and Shapley, 1996] Dov Monderer and Lloyd S. Shapley. Potential games. Games and Economic Behavior, 14:124-143, 1996.","title":"Potential games","authors":"Shapley Monderer, Dov Monderer, Lloyd S Shapley","year":"1996","venue":"Games and Economic Behavior","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Myerson, 1991] Roger B. Myerson. Game theory -Analy- sis of conflict. Harvard University Press, 1991.","title":"Game theory -Analysis of conflict","authors":"B Roger, Myerson","year":"1991","venue":null,"doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Nash, 1950] John Nash. Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1):48-49, 1950.","title":"John Nash. Equilibrium points in n-person games","authors":"Nash","year":"1950","venue":"Proceedings of the National Academy of Sciences","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Nisan et al., 2007] Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani. Algorithmic Game Theory. Cambridge University Press, 2007.","title":"Algorithmic Game Theory","authors":"Nisan","year":"2007","venue":null,"doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Osborne and Rubinstein, 1994] Martin J. Osborne and Ariel Rubinstein. A Course in Game Theory. MIT, Cambridge, MA, 1994.","title":"A Course in Game Theory","authors":"Martin J Osborne, Ariel Rubinstein","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Ouenniche et al., 2016] Jamal Ouenniche, Aristotelis Boukouras, and Mohammad Rajabi. An ordinal game theory approach to the analysis and selection of parten- ers in public-private partnership projects. Journal of Optimization Theory and Applications, 169:314-343, 2016.","title":"Jamal Ouenniche, Aristotelis Boukouras, and Mohammad Rajabi. An ordinal game theory approach to the analysis and selection of parteners in public-private partnership projects","authors":"Ouenniche","year":"2016","venue":"Journal of Optimization Theory and Applications","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Puterman, 1994] Martin L. Puterman. Markov Decision Processes. John Wiley and Sons, 1994.","title":"Markov Decision Processes","authors":"Martin L Puterman","year":"1994","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Sabbadin et al., 1998] Régis Sabbadin, Hélène Fargier, and Jérôme Lang. Towards qualitative approaches to multi- stage decision making. International Journal of Approxi- mate Reasoning, 19:441-471, 1998.","title":"Towards qualitative approaches to multistage decision making","authors":"Régis Sabbadin, Hélène Fargier, Jérôme Lang","year":"1998","venue":"International Journal of Approximate Reasoning","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Sabbadin, 2001] Régis Sabbadin. Possibilistic Markov de- cision processes. Engineering Applications of Artificial Intelligence, 14:287-300, 2001.","title":"Possibilistic Markov decision processes","authors":"Régis Sabbadin","year":"2001","venue":"Engineering Applications of Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Sorin, 2002] Sylvain Sorin. A first course in zero-sum re- peated games. Springer, 2002.","title":"A first course in zero-sum repeated games","authors":"Sylvain Sorin","year":"2002","venue":null,"doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Von Neumann and Morgenstern, 1948] John Von Neumann and Oskar Morgenstern. Theory of games and economic behavior. 1948.","title":"John Von Neumann and Oskar Morgenstern","authors":"Von Neumann, Morgenstern","year":"1948","venue":"Theory of games and economic behavior","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Xu, 2000] Chunhui Xu. Computation of noncooperative equilibria in ordinal games. European Journal of Oper- ational Research, 122:115-122, 2000.","title":"Computation of noncooperative equilibria in ordinal games","authors":"Chunhui Xu, Xu","year":"2000","venue":"European Journal of Operational Research","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}