Allocation rules for network games with local considerations

We introduce a new allocation rule for network games that combines a local component and a global component. The local component depends only on the links incident to each player, whereas the global component allocates a surplus equally among the members of each connected component. We characterize this allocation rule by three classical axioms together with a new axiom, Fairness under Neighborhood Restriction, which requires that two adjacent players experience the same payoff variation when the network is restricted to their local neighborhoods, that is, to the sets of links incident to each player. We also examine an alternative allocation rule that differs only in its global component, distributing the surplus within each connected component in proportion to players’ degrees in the network.