0511152 20240103222930.120191118235959.9 85066154003 000496600500006 10.1007/s00186-019-00672-y 29 s. P cav_un_epca*02542751432-2994902 (2019)271-300Springer coalitional game totally balanced game balanced system polyhedral cone cav_un_auth*0101141 Kroupa Tomáš 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*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. http://library.utia.cas.cz/separaty/2019/MTR/kroupa-0511152.pdf https://link.springer.com/article/10.1007%2Fs00186-019-00672-y cav_un_auth*0332303 GA16-12010S GA ČR CZ The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every totally balanced game is also representable as the minimum of a finite set of additive games. In this paper we characterize the polyhedral cone of totally balanced games by describing its facets. Our main result is that there is a correspondence between facet-defining inequalities for the cone and the class of special balanced systems of coalitions, the so-called irreducible min-balanced systems. Our method is based on refining the notion of balancedness introduced by Shapley. We also formulate a conjecture about what are the facets of the cone of exact games, which addresses an open problem appearing in the literature. WOS BA 10000 10100 10101 2020 2 RVO:67985556 http://hdl.handle.net/11104/0302521 S 3+4 Review Biochemistry Molecular Biology|Chemistry Multidisciplinary C OPERATIONSRESEARCH&MANAGEMENTSCIENCE|MATHEMATICS.APPLIED 1.163 0.171 12.5 0.00155 0.668 1048 56 0.769 32.77 1.16 190 Q2 0.963 35 Q3 47.434 29.5 Q3 Q4 0.53 Q3 40.421 2019 85066154003 SCOPUS PUBMED 000496600500006 WOS cav_un_epca*0254275 Mathematical Methods of Operations Research 1432-2994 1432-5217 Roč. 90 č. 2 2019 271 300 Springer