0478360 20240103214537.120170922235959.9 85069445814 12 s. P cav_un_epca*0478359Proceedings of the 10th International Symposium on Imprecise Probability: Theories and Applications313-324LuganoPMLR2017AntonucciA.CoraniG.CousoI.DesterckeS. extreme exact game coherent lower probability core credal set supermodular game 2-monotone lower probability min-representation oxytrophic game cav_un_auth*0101202 Department of Decision Making Theory Studený Milan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Department of Decision Making Theory Kratochvíl Václav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR CZ Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2017/MTR/studeny-0478360.pdf cav_un_auth*0332303 GA16-12010S GA ČR CZ The notion of a (discrete) coherent lower probability corresponds to a game-theoretical concept of an exact (cooperative) game. The collection of (standardized) exact games forms a pointed polyhedral cone and the paper is devoted to the extreme rays of that cone, known as extreme exact games. A criterion is introduced for testing whether an exact game is extreme. The criterion leads to solving simple linear equation systems determined by (the vertices of) the core polytope (of the game), which concept corresponds to the notion of an induced credal set in the context of imprecise probabilities. The criterion extends and modifies a former necessary and sufficient condition for the extremity of a supermodular game, which concept corresponds to the notion of a 2-monotone lower probability. The linear condition we give in this paper is shown to be necessary for an exact game to be extreme. We also know that the condition is sufficient for the extremity of an exact game in an important special case. The criterion has been implemented on a computer and we have made a few observations on basis of our computational experiments. cav_un_auth*0350127 ISISPTA 2017 - International Symposium on Imprecise Probability: Theories and Applications /10./ 20170710 20170714 Lugano CH BA 2018 2 PR RVO:67985556 http://hdl.handle.net/11104/0274593 S 2017 85069445814 SCOPUS PUBMED WOS cav_un_epca*0478359 Proceedings of the 10th International Symposium on Imprecise Probability: Theories and Applications PMLR 2017 Lugano 313 324 Proceedings of Machine Learning Research volume 62 1938-7228 340 Antonucci A. 340 Corani G. 340 Couso I. 340 Destercke S.