Contagion risks and security investment in directed networks.

Area of Science:

• Network Science
• Risk Analysis
• Game Theory

Background:

• Existing contagion models like independent cascade and linear threshold have limitations.
• Understanding contagion amplification in complex networks is crucial for risk management.

Purpose of the Study:

• To develop a generalized model for contagion risks and optimal security investment in directed networks.
• To analyze network resilience and the impact of interventions.
• To study Nash equilibrium and socially optimal security investment strategies.

Main Methods:

• Developed a generalized contagion model for interconnected agents with heterogeneous properties.
• Stated limit theorems for final contagion size in random networks with various degree distributions.
• Analyzed asymptotic Nash equilibrium and socially optimal investment using network vulnerability.

Main Results:

• Derived network resilience conditions and quantified contagion amplification.
• Showed that infinite variance degree distributions with correlated degrees can trigger widespread contagion.
• Demonstrated the impact of interventions (percolation) on contagion spread.
• Identified network vulnerability as a key factor in agents' risk and investment decisions.
• Provided conditions for unique and monotone Nash equilibrium in security investment.

Conclusions:

• The model offers a generalized framework for contagion and investment analysis.
• Network structure significantly influences contagion amplification and resilience.
• Network vulnerability provides a tractable approach to analyzing security investment equilibrium.