The neighborhood value for cooperative graph games

We consider cooperative games with a neighborhood structure modeled by a graph. Our approach shares some similarities with the models of graph games (Myerson, 1977) and games with a local permission structure (van den Brink and Dietz, 2014). The value that we study shares the Harsanyi dividend of each coalition equally among the coalition members and their neighbors. We characterize this value by five axioms: Efficiency, Additivity, Null neighborhood out (removing a null player whose neighbors are also null does not affect the remaining players' payoffs), Equal loss in an essential situation (if a single coalition has a non-null Harsanyi dividend and the other players are neighbors of that coalition, removing any player induces the same payoff variation for the remaining players) and Two-player symmetry (In a two-player game, the players obtain equal payoffs if they are symmetric or neighbors).