The locally partial permission value for games with a permission structure

Cooperative games with a permission structure are useful tools for analyzing the impact of hierarchical structures on allocation problems in Economics and Operations Research. In this paper, we propose a generalization of the local disjunctive and the local conjunctive permission approaches called the k-local permission approach. In this approach, every player needs permission from a certain number of its predecessors to cooperate in a coalition. The special case where every player needs permission from at least one of, respectively all, its predecessors coincides with the local disjunctive, respectively local conjunctive, approach in the literature. We de ne and characterize a corresponding k-local permission value. After that, we apply this value to de ne a new class of power measures for directed graphs. We axiomatize these power measures, and apply some of them to two classical networks in the literature.