Many economic and social networks share two common organizing features: (1) a core-periphery structure; (2) positive correlation between network centrality and payoffs. In this paper, we build a model of network formation where these features emerge endogenously. In our model, the unique equilibrium network architecture is a periphery-sponsored star. In this equilibrium, one player, the center, maintains no links and achieves a high payoff, while all other players maintain a single link to the center and achieve lower payoffs. With heterogeneous groups, equilibrium networks are interconnected stars. We show that small minorities tend to integrate while large minorities are self-sufficient. Although any player can be the center in a static equilibrium, evolution selects the agent with most valuable resources as the center in the long run. In particular, even small inequalities in resources can lead to large payoff inequality because of the endogenous social structure. Our main results are robust to the introduction of transfers and bargaining over link costs.
