We present a set-theoretical characterization of a bound on the maximal portion that an agent can cede of its input variable to another agent. By ceding control authority, agents can decompose coupling variables into public and private parts, which is of interest in situations of partial cooperation. In particular, sufficient conditions under which the non-existence of the maximum robust control invariant set is guaranteed are provided, expressed in terms of support functions and the dominant system eigenvalue. Finally, the results are illustrated via stable and unstable example systems with different coupling.