  The emergence of large-scale connectivity underlies the proper functioning of
many networked systems, ranging from social networks and technological
infrastructure to global trade networks. Percolation theory characterizes
network formation following stochastic local rules, while optimization models
of network formation assume a single controlling authority or one global
objective function. In socio-economic networks, however, network formation is
often driven by individual, locally optimal decisions. How such decisions
impact connectivity is only poorly understood to date. Here, we study how
large-scale connectivity emerges from decisions made by rational agents that
individually minimize costs for satisfying their demand. We establish that the
solution of the resulting nonlinear optimization model is exactly given by the
final state of a local percolation process. This allows us to systematically
analyze how locally optimal decisions on the micro-level define the structure
of networks on the macroscopic scale.
