Fair allocation in networks with externalities

I prove existence and uniqueness of a component efficient and fair allocation rule when the value of the network is allowed to exhibit any type of externalities across its components. This is done by means of a new specification of the value function, generalizing partial results appearing in Myerson [Myerson, R.B., 1977a. Graphs and cooperation in games. Math. Operations Res. 2, 225-229], Feldman [Feldman, B.E., 1996. Bargaining, coalition formation and value. PhD dissertation. State University of New York at Stony Brook] and Jackson and Wolinsky [Jackson, M.O., Wolinsky, A., 1996. A strategic model of social and economic networks. J. Econ. Theory 71, 44-74]. This component efficient and fair allocation rule is found closely related to an extension of the Shapley value to TU-games in partition function form proposed by Myerson [Myerson, R.B., 1977b. Values of games in partition function form. Int. J. Game Theory 6 (1), 23-31].