Coevolutionary game dynamics with local and global environmental feedbacks on spatially embedded networks.

In recent years, the coevolutionary dynamics between game strategies and environmental states have attracted considerable attention. Most existing relevant studies focus on well-mixed populations or regular lattices and have yet to systematically investigate strategy-environment coevolutionary dynamics on complex spatial structures. In this work, we construct spatially embedded networks with three typical degree distributions (delta, Poisson, and power-law distributions), based on which we establish a multi-agent coevolutionary model with local and global environmental feedbacks. Using Monte Carlo simulations, we investigate the impacts of degree heterogeneity, average degree, and random connectivity on system dynamics. Simulation results show that the degree distribution significantly alters the system's dynamical behaviors. Among the three network topologies, homogeneous-degree networks are most conducive to dynamical stability. Moreover, average degree exerts a universal effect across all networks: cooperation level follows a unimodal trend, increasing first and then decreasing as average degree increases, with the maximum achieved at an intermediate average degree. This study explores how spatially embedded networks shape coevolutionary game dynamics and offers insights into the evolution of cooperation in complex adaptive systems.