A general characterization for non-balanced games in terms of U-cycles

Juan Carlos Cesco

European Journal of Operational Research, 2008, vol. 191, issue 2, pages 409-415

Abstract: In a paper by Cesco [Cesco, J.C., 2003. Fundamental cycles of pre-imputations in non-balanced TU-games. International Journal of Game Theory 32, 211-222], it was proven that the existence of a certain type of cycles of pre-imputations, fundamental cycles, is equivalent to the non-balancedness of a TU-game, i.e., the emptiness of the core of the game. There are two characteristic sub-classes related to fundamental cycles: U-cycles and maximal U-cycles. In this note we show that it is enough to consider U-cycles in obtaining a similar characterization for non-balanced TU-games.

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