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

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  • Cesco, Juan Carlos

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.

Suggested Citation

  • Cesco, Juan Carlos, 2008. "A general characterization for non-balanced games in terms of U-cycles," European Journal of Operational Research, Elsevier, vol. 191(2), pages 409-415, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:409-415
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    References listed on IDEAS

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    1. Juan Carlos Cesco, 2003. "Fundamental cycles of pre-imputations in non-balanced TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 211-221, December.
    2. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    3. Sengupta, Abhijit & Sengupta, Kunal, 1994. "Viable Proposals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 347-359, May.
    4. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    5. Xiaotie Deng & Christos H. Papadimitriou, 1994. "On the Complexity of Cooperative Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 257-266, May.
    6. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 2001. "On the computation of the nucleolus of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 79-98.
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