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On the 1-Nucleolus for Classes of Cooperative Games

Author

Listed:
  • A. Estévez-Fernández

    (VU University Amsterdam, the Netherlands)

  • P. Borm

    (Tilburg University, the Netherlands)

  • M.G. Fiestras-Janeiro

    (Universidade de Vigo, Spain)

  • M.A. Mosquera

    (Universidade de Vigo, Spain)

  • E. Sánchez-Rodríguez

    (Universidade de Vigo, Spain)

Abstract

This paper analyzes the 1-nucleolus and, in particular, its relation to the nucleolus and compromise value. It is seen that the 1-nucleolus of a cooperative game can be characterized using a combination of standard bankruptcy rules for associated bankruptcy problems. In particular, for any zero-normalized balanced game, the 1-nucleolus coincides with the Aumann-Maschler rule (Aumann and Maschler, 1985} in this sense. From this result, not only necessary conditions on a compromise stable game are derived such that the 1-nucleolus and the nucleolus coincide, but also necessary and sufficient conditions such that the 1-nucleolus and the compromise value of exact games coincide.

Suggested Citation

  • A. Estévez-Fernández & P. Borm & M.G. Fiestras-Janeiro & M.A. Mosquera & E. Sánchez-Rodríguez, 2015. "On the 1-Nucleolus for Classes of Cooperative Games," Tinbergen Institute Discussion Papers 15-123/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20150123
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    Keywords

    1-nucleolus; Compromise stable games; Exact games; Aumann-Maschler rule; Nucleolus; Compromise value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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