Solidarity within a fixed community

- We study the consequences of a player becoming a null player.
- Nullified solidarity: in this case, either all players weakly gain or all weakly lose.
- We provide a new characterization of the equal division value.
- It uses efficiency, the null game property, weak fairness, and nullified solidarity.

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 lose together. Combined with efficiency, the null game property, and a weak fairness property, we obtain a new characterization of the equal division value.