Estévez-Fernández, A. Borm, P. Fiestras-Janeiro, M.G. Mosquera, M.A. Sánchez-Rodríguez, E.
Year of Publication:
Tinbergen Institute Discussion Paper 15-123/II
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.
1-nucleolus Compromise stable games Exact games Aumann-Maschler rule Nucleolus Compromise value