Hysteretic percolation from locally optimal individual decisions

TL;DR

This paper explores how individual, cost-minimizing decisions by rational agents influence the emergence of large-scale connectivity in networks, linking local optimization to global percolation phenomena.

Contribution

It introduces a nonlinear optimization model showing that local decision-making leads to a percolation process, bridging micro-level choices and macro-level network structure.

Findings

Locally optimal decisions determine the network's large-scale connectivity.

The model exactly maps to a local percolation process.

Insights into how individual choices shape global network properties.

Abstract

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.