The positive core of a cooperative game

The positive core is a nonempty extension of the core of transferable utility games. If the core is nonempty, then it coincides with the core. It shares many properties with the core. Six well-known axioms which are employed in some axiomatizations of the core, the prenucleolus, or the positive prekernel, and one new intuitive axiom, characterize the positive core on any infinite universe of players. This new axiom requires that the solution of a game, whenever it is nonempty, contains an element which is invariant under any symmetry of the game.