Allocating value among farsighted players in network formation

•We study the stability of networks when players are farsighted.•Allocations are determined endogenously.•We propose the notion of von Neumann-Morgenstern farsighted stability with bargaining.•Stability singles out the set of strongly efficient networks under some conditions.•The componentwise egalitarian allocation rule emerges endogenously.

We study the stability of networks when players are farsighted and allocations are determined endogenously. The set of strongly efficient networks is the unique von Neumann-Morgenstern farsightedly stable set with bargaining if the value function is anonymous, component additive and top convex and the allocation rule is anonymous and component efficient. Moreover, the componentwise egalitarian allocation rule emerges endogenously.