Facets of the cone of totally balanced games

0511152 - ÚTIA 2020 RIV DE eng J - Journal Article
Kroupa, Tomáš - Studený, Milan
Facets of the cone of totally balanced games.
Mathematical Methods of Operations Research. Roč. 90, č. 2 (2019), s. 271-300. ISSN 1432-2994. E-ISSN 1432-5217
R&D Projects: GA ČR(CZ) GA16-12010S
Institutional support: RVO:67985556
Keywords : coalitional game * totally balanced game * balanced system * polyhedral cone
OECD category: Pure mathematics
Impact factor: 1.000, year: 2019
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/MTR/kroupa-0511152.pdf https://link.springer.com/article/10.1007%2Fs00186-019-00672-y

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.
Permanent Link: http://hdl.handle.net/11104/0302521