One-Way Flow Networks with Decreasing Returns to Linking

This paper presents a model of noncooperative network formation in which the benefit of new links eventually decreases. Agents link with each other to gain information and update their links according to better-reply dynamics. We show that all equilibrium networks display a center-periphery structure and may be disconnected. The only equilibrium networks that satisfy some strictness conditions are constellations of starred wheels, where central agents form possibly several optimally sized disjoint wheels and peripheral agents are linked to one of the wheels from outside. In the long run, the system settles to such a network architecture. The main features of a constellation of starred wheels are reminiscent of some well-known real-world facts. Collections of smaller disjoint networks connecting only a few agents are more common than global networks connecting all the agents in a community. Also differences within a connected component such as the center and the periphery are often found.