In this paper we prove a characterization for the subclass of non-balanced TU-games. The result is stated in terms of certain class of cycles of pre-imputations. A cycle is a finite sequence of pre-imputations, where each pair of neighbouring elements are interrelated to each other through a transfer of some amount of utility from members of a certain coalition to the members of the complementary coalition, with the understanding that individual gains or losses within any coalition are proportional to the number of members of the coalition. These cycles are strongly connected with a transfer scheme designed to reach a point in the core of a TU-game provided this set is non-empty. The main result of this paper provides an alternative characterization of balanced TU-games to Shapley–Bondareva's theorem.
