Convergence analysis of distributed population dynamics based on second-order Delaunay triangulation

This article proposes a second-order communication network generation method based on Delaunay triangulation for a large-scale population. Given the complexity of communication network characteristics, the relationship between network topology and the convergence of Nash equilibrium needs further exploration. We propose a network generation method based on Delaunay triangulation to ensure the Nash equilibrium convergence of population dynamics. To speed the convergence of large-scale populations, we introduce a second-order communication network and form the distributed population dynamics for investigation. We also design a learning rule for strategic interactions to fit the second-order network population. The corresponding Nash equilibrium can converge from the perspectives of both numerical analysis and simulation results. In addition, we explore how the learning intensity influences the evolutionary process. These results may provide new ideas for guaranteeing convergence and developing the strategic interaction rule.