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.
# 15-123/II (2015-11-02)
- 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
- 1-nucleolus, Compromise stable games, Exact games, Aumann-Maschler rule, Nucleolus, Compromise value
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