The equity core and the core

In this paper we study the equity core (Selten, 1978) and compare it with the core. A payoff vector is in the equity core if no coalition can divide its value among its members proportionally to a given weight system and, in this way, give more to each member than the amount he or she receives in the payoff vector. We show that the equity core is a compact extension of the core and that, for non-negative games, the intersection of all equity cores with respect to all weights coincides with the core of the game.