Linear core-based criterion for testing extreme exact games

0478360 - ÚTIA 2018 GB eng C - Konferenční příspěvek (zahraniční konf.)
Studený, Milan - Kratochvíl, Václav
Linear core-based criterion for testing extreme exact games.
Proceedings of the 10th International Symposium on Imprecise Probability: Theories and Applications. Lugano: PMLR, 2017 - (Antonucci, A.; Corani, G.; Couso, I.; Destercke, S.), s. 313-324. Proceedings of Machine Learning Research, volume 62. E-ISSN 1938-7228.
[ISISPTA 2017 - International Symposium on Imprecise Probability: Theories and Applications /10./. Lugano (CH), 10.07.2017-14.07.2017]
Grant CEP: GA ČR(CZ) GA16-12010S
Institucionální podpora: RVO:67985556
Klíčová slova: extreme exact game * coherent lower probability * core * credal set * supermodular game * 2-monotone lower probability * min-representation * oxytrophic game
Kód oboru RIV: BA - Obecná matematika
http://library.utia.cas.cz/separaty/2017/MTR/studeny-0478360.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0274593