Hysteretic Percolation from Locally Optimal Individual Decisions.

Area of Science:

• Network science
• Socioeconomic systems
• Complexity science

Background:

• Large-scale connectivity is crucial for many systems, from social networks to global trade.
• Existing models like percolation theory and optimization models have limitations in explaining socioeconomic network formation.
• Socioeconomic networks often form through individual, locally optimal decisions, a process poorly understood.

Purpose of the Study:

• To investigate how large-scale connectivity emerges from individual rational decisions in socioeconomic networks.
• To bridge the gap between micro-level decision-making and macro-level network structure.
• To provide a theoretical framework for analyzing emergent network properties.

Main Methods:

• Developed a nonlinear optimization model based on rational agents minimizing costs.
• Analyzed the emergent network structure resulting from these individual decisions.
• Established a formal link between the optimization model's solution and a local percolation process.

Main Results:

• The solution to the nonlinear optimization model precisely matches the final state of a local percolation process.
• Demonstrated that locally optimal decisions by rational agents lead to predictable large-scale connectivity patterns.
• Provided a method to systematically analyze how micro-level choices shape macro-level network topology.

Conclusions:

• Individual, cost-minimizing decisions in socioeconomic networks can lead to emergent large-scale connectivity.
• The study unifies concepts from optimization and percolation theory to explain network formation.
• This framework offers new insights into the structure and function of complex socioeconomic systems.