This paper characterizes the set of equilibrium networks in the two-way flow model of network formation with small decay, and this for all increasing benefit functions of the players. We show that as long as the population is large enough, this set contains large- as well as small-diameter networks. For all benefit functions, the periphery-sponsored star is the most stable. When the marginal benefits of information are constant, all non-star networks are equally stable. With increasing marginal benefits of information, small-diameter networks in general tend to be more stable. However, with decreasing marginal benefits of information, large-diameter networks tend to be the most robust along with the periphery-sponsored star.
Network formation two-way flow model decay non-linear benefits