0556097 20230418204736.920220329235959.9 85124749808 000757714500001 10.1007/s00186-022-00770-4 46 s. P cav_un_epca*02542751432-2994951 (2022)35-80Springer coalitional game exact game totally balanced game anti-dual of a game semi-balanced set system indecomposable min-semi-balanced system cav_un_auth*0101202 Studený Milan UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0216188 Kratochvíl Václav UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory CZ Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2022/MTR/studeny-0556097.pdf https://link.springer.com/article/10.1007/s00186-022-00770-4 GA19-04579S GA ČR CZ cav_un_auth*0380558 The class of exact transferable utility coalitional games, introduced in 1972 by Schmeidler, has been studied both in the context of game theory and in the context of imprecise probabilities. We characterize the cone of exact games by describing the minimal set of linear inequalities defining this cone. These facet-defining inequalities for the exact cone appear to correspond to certain set systems (= systems of coalitions). We noticed that non-empty proper coalitions having non-zero coefficients in these facet-defining inequalities form set systems with particular properties. More specifically, we introduce the concept of a semi-balanced system of coalitions, which generalizes the classic concept of a balanced coalitional system in cooperative game theory. The semi-balanced coalitional systems provide valid inequalities for the exact cone and minimal semi-balanced systems (in the sense of inclusion of set systems) characterize this cone. We also introduce basic classification of minimal semi-balanced systems, their pictorial representatives and a substantial concept of an indecomposable (minimal) semi-balanced system of coalitions. The main result of the paper is that indecomposable semi-balanced systems are in one-to-one correspondence with facet-defining inequalities for the exact cone. The second relevant result is the rebuttal of a former conjecture claiming that a coalitional game is exact iff it is totally balanced and its anti-dual is also totally balanced. We additionally characterize those inequalities which are facet-defining both for the cone of exact games and for the cone of totally balanced games. WOS BA 10000 10100 10101 2023 2 RVO:67985556 http://hdl.handle.net/11104/0330491 S 3+4 Article Operations Research Management Science|Mathematics Applied C OPERATIONSRESEARCH&MANAGEMENTSCIENCE|MATHEMATICS.APPLIED 1.1 0.1 14.5 0.00089 0.508 1125 0.554 1.200 38 Q3 28.3 Q3 Q3 0.4 Q3 45.5 2022 85124749808 SCOPUS PUBMED 000757714500001 WOS cav_un_epca*0254275 Mathematical Methods of Operations Research 1432-2994 1432-5217 Roč. 95 č. 1 2022 35 80 Springer