A note on the characterization of Nash networks

In the present paper, we are interested in the one-way flow model of Bala and Goyal (2000) [Bala, V., Goyal, S., 2000. A non-cooperative model of network formation, Econometrica, N. 68 (5), 1181-1229]. We generalize this model by relaxing the authors' assumption concerning the relation between the number of resources obtained by an agent and this agent's payoffs. Firstly, we show that Nash networks are line bases and strict Nash networks are minimum line bases. Secondly, we establish that efficient networks are minimum line bases.