---

The emergence of global structures in networks is at the core of our increasingly connected world, ranging from international trade to the spreading of innovations in social networks. Many of these networks are constructed by individual decisions optimizing connectivity under various constraints, for example people choosing their friends in geographically constrained social networks. Yet, how and under which conditions these local decisions create global structures is hardly understood. We study a general optimization problem modeling the emergence of global interactions in networks in the presence of local feedback and transaction costs over long distances. Related problems arise for economic decisions in trade networks, for biological interactions in the context of cooperation and in social networks for the adoption of innovations. We map a wide range of these global optimization problems to a local percolation model where connectivity increases when the transaction costs in the network decrease. We explain how this transition is affected by the network structure and the local feedback effects: While the transition is discontinuous in compact networks and for strong enough feedback effects, the transition is slow in networks with a large diameter and small feedback effects.

---

Malte Schröder, Max Planck Institute for Dynamics and Self-Organization Göttingen
Institute for theoretical Physics (New Building), Room 0.01
Contact: Dirk Witthaut