A Core Concept for Partition Function Games

In this paper, we introduce a new core concept for partition function games, to be called the strong-core, which reduces to the ordinary core if the worth of every coalition is independent of the partitions to which it belongs and the game is adequately represented by a characteristic function. It is nicely related to previous core concepts, but unlike them does not assume formation of a specific partition subsequent to a deviation from the grand coalition. We show that a prominent class of partition function games admit nonempty strong-cores and derive alternative sufficient conditions for a partition function game to admit a nonempty strong-core which can be applied to games with negative or positive externalities. We justify the strong-core also as a non-cooperative solution concept by showing that a set of strong-core payoff vectors can be supported as equilibrium outcomes of an infinitely repeated game. JEL classification numbers: C70-73