Allocation rules for communication situations with incompatibilities

In this article we analyze certain situations with restricted cooperation. To do this we introduce a model that combines two types of games well studied in the literature: graph-restricted games and games with incompatible players. In particular, our model extends Myerson’s model for communication situations and Bergantiños’ model for incompatible relationships. Our approach is based on the concept of profit measure, which allows us to deal simultaneously with both types of bilateral relationships. We show that in the situations considered there are multiple possible definitions of the profit achievable for each coalition. This leads us to introduce different allocation rules for these cooperative situations.