k-boundedness, feasible communication structures, and the Myerson value

In cooperative games with communication networks, it is typically assumed that two players can communicate whenever there is a connecting path between them, regardless of its length. We relax this assumption by introducing a new concept, k-boundedness, which sets an upper bound on the length of admissible communication paths. Building on this idea, we define a restriction operator for feasible coalitions in communication games, which leads to a new solution concept extending the Myerson value. Our first main contribution is an axiomatic characterization of this solution within the class of games with communication networks. The characterization combines the classical Fairness axiom with new axioms capturing the effect of k-boundedness constraints on cooperative possibilities. We then investigate the feasible coalition structures that arise under arbitrary k-boundedness constraints, which we term feasible communication structures. Within this alternative framework, we provide another axiomatic characterization of our solution concept.