  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.
