U-cycles in n-person TU-games with equal-sized objectionable families of coalitions

• Autores: Cesco, Juan Carlos; Calí, Ana L.
• Año de publicación: 2009
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: NON BALANCED GAMES; CYCLES; TRANSFER SCHEME
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

It has recently been proven that the non-existence of certain types of cycles of pre-imputation, fundamental cycles, is equivalent to the balancedness of a TU-game (see [3]). In some cases, the class of fundamental cycles can be narrowed and a characterization theorem may still be obtained. In this paper, we deal with n-person TU-games for which the only coalitions with nonzero value, aside from the grand coalition, are all coalitions of the same size k ≤ n, which also form a balanced family of coalitions. This class of games includes those studied in previous papers where the non-zero value coalitions are the family of coalitions with n − 1 players. The main result obtained in this framework is that it is always possible to find a U-cycle, a certain type of fundamental cycle, provided the game under consideration is non-balanced and n and k are relatively prime. A computational procedure to get the cycle is provided as well. In many situations, these cycles turn out to be maximal U-cycles, an even more restricted class of fundamental cycles.
Fil: Cesco, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Calí, Ana L.. Universidad Nacional de San Luis; Argentina