0490915 20240111141003.420180710235959.9 11 s. P cav_un_epca*0490306978-80-7378-361-7177-187PrahaMatfyzPress, Publishing House of the Faculty of Mathematics and Physics Charles University2018KratochvílVáclavVejnarováJiřina exact game extremity irreducible balanced cav_un_auth*0101202 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 34 Studený Milan UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101141 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 33 Kroupa Tomáš UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory 33 Kratochvíl Václav UTIA-B CZ Ústav teorie informace a automatizace AV ČR, v. v. i. PDF http://library.utia.cas.cz/separaty/2018/MTR/studeny-0490915.pdf GA16-12010S GA ČR CZ cav_un_auth*0332303 The sets of balanced, totally balanced, exact and supermodular games play an important role in cooperative game theory. These sets of games are known to be polyhedral cones. The (unique) non-redundant description of these cones by means of the so-called facet-defining inequalities is known in cases of balanced games and supermodular games, respectively. The facet description of the cones of exact games and totally balanced games are not known and we present conjectures about what are the facet-defining inequalities for these cones. We introduce the concept of an irreducible min-balanced set system and conjecture that the facet-defining inequalities for the cone of totally balanced games correspond to these set systems. The conjecture concerning exact games is that the facet-defining inequalities for this cone are those which correspond to irreducible min-balanced systems on strict subsets of the set of players and their conjugate inequalities. A consequence of the validity of the conjectures would be a novel result saying that a game m is exact if and only if m and its reflection are totally balanced. cav_un_auth*0361637 Workshop on Uncertainty Processing (WUPES’18) 20180606 Třeboň CZ 20180609 BA 10000 10100 10101 2019 3 PR RVO:67985556 http://hdl.handle.net/11104/0285278 S 16 2018 SCOPUS PUBMED WOS PDF cav_un_epca*0490306 Proceedings of the 11th Workshop on Uncertainty Processing (WUPES’18) MatfyzPress, Publishing House of the Faculty of Mathematics and Physics Charles University 2018 Praha 177 187 978-80-7378-361-7 340 Kratochvíl Václav 340 Vejnarová Jiřina