In this paper we study cooperative games with limited cooperation possibilities, represented by an undirected cycle-free communication graph. Players in the game can cooperate if and only if they are connected in the graph. We introduce a new single-valued solution concept, the average tree solution. Our solution is characterized by component efficiency and component fairness. The interpretation of component fairness is that deleting a link between two players yields for both resulting components the same average change in payoff, where the average is taken over the players in the component. The average tree solution is always in the core of the restricted game and can be easily computed as the average of n specific marginal vectors, where n is the number of players. We also show that the average tree solution can be generated by a specific distribution of the harsanyi dividends.