Emergence of a complex network structure on a Spatial Prisoner's Dilemma.

Area of Science:

• Complex Systems
• Game Theory
• Network Science

Background:

• Spatial game theory on networks is well-studied.
• Heterogeneous network structures influence population dynamics.
• Few models integrate population evolution, network growth, and player decision-making.

Purpose of the Study:

• To model spatial prisoner's dilemma on a random network with dynamic player strategies and network evolution.
• To investigate how individual decision-making impacts network structure and population dynamics.
• To explore the emergence of network properties under evolutionary game theory.

Main Methods:

• Utilized a spatial prisoner's dilemma model on a random network.
• Incorporated player access to recent past information for strategy adoption.
• Implemented a link evolution mechanism where players alter neighbors based on low payoffs.
• Simulated scenarios including an "unlikely to happen" strategy adoption.

Main Results:

• The model spontaneously evolved into an approximate scale-free network near a critical parameter.
• Hub players demonstrated dynamic behavior, sometimes decreasing their node degree.
• The interplay between strategy adoption and network evolution was observed.

Conclusions:

• Dynamic player decision-making and network evolution can lead to scale-free network structures.
• Hub players are not static and can adapt their connectivity, influencing system resilience.
• The model provides insights into the co-evolution of behavior and network topology in complex systems.