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, Math. Oper. Res. 2 (1977) 225–229] and games with a local permission structure [van den Brink and Dietz, Theory Decis . 76 (2014) 343–361]. 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).