Cooperation when some players are incompatible

A situation with incompatibilities is defined to be a TU-game together with a graph whose arcs link pairs of incompatible players. In this paper the authors introduce an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and prove that it is uniquely determined. Besides, they demonstrate that it is stable, study its relationship with the so-called IR-Shapley value and show that it generalizes an earlier theory for simple games. Finally, the communication situations with incompatibilities are studied.