Abstract
To solve the problems about the emptiness and nonexistence of the recursive core (r-core) as introduced by Huang and Sjöström (2003), this paper considers a new recursive solution concept for partition function form games: the recursive nucleolus (r-nucleolus). In each recursive step, the prediction of a coalition about the partition of outsiders is consistent with the nucleolus in characteristic function form games. We show that the r-nucleolus is always nonempty, and it is a singleton in fully cohesive partition function form games. A sufficient condition is then provided to show that the r-nucleolus is included in the r-core. Additionally, some desirable properties that the r-nucleolus satisfies are presented. Moreover, we discuss applications of the r-nucleolus in Cournot oligopoly and Bertrand competition.
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