U-cycles in n-person TU games with only 1, n-1 and n-person permissible coalitions

Abstract

It has been recently proved that the non-existence of certain type of cycles of pre-imputation, fundamental cycles, is equivalent to the balancedness of a TU-games (Cesco (2003)). In some cases, the class of fundamental cycles can be narrowed and still obtain a characterization theorem. In this paper we prove that existence of maximal U-cycles, which are related to a transfer scheme designed for computing a point in the core of a game, is condition necessary and sufficient for a TU-game be non-balanced, provided n-1 and n-person are the only coalitions with non-zero value. These games are strongly related to games with only 1, n-1 and n-person permissible coalitions (Maschler (1963)).