We study the consequences of a solidarity property that specifies how a value for cooperative games should respond if some player forfeits his productivity, i.e., becomes a null player. Nullified solidarity states that in this case either all players weakly gain together or all players weakly...

The Shapley value probably is the most eminent single-point solution concept for TU-games. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players...

The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player's marginal contribution to all coalitions increase or stay the same, then this player's payoff should not decrease. We investigate the class of values...

We provide new characterisations of the equal surplus division value. This way, the difference between the Shapley value, the equal surplus division value, and the equal division value is pinpointed to one axiom.

We suggest a new one-parameter family of solidarity values for TU-games. The members of this class are distinguished by the type of player whose removal from a game does not affect the remaining players’ payoffs. While the Shapley value and the equal division value are the boundary members of...