The Positive Prekernel of a Cooperative Game

Peter Sudholter & Bezalel Peleg

The positive prekernel, a solution of cooperative transferable utility games, is introduced. We show that this solution inherits many properties of the prekernel and of the core, which both are subsolutions. It coincides with its individually rational variant, the positive kernel, when applied to any zero-monotonic game. The positive (pre)kernel is a subsolution of the reactive (pre) bargaining set. We prove that the positive prekernel on the set of games with players belonging to a universe of at least three possible members can be axiomatized by nonemptiness, anonymity, reasonablenss, the weak reduced game property, the converse reduced game property, and a weak version of unanimity for two-person games.

December, 2000
Published in: 
International Game Theory Review 2 (2000), 287-305