Spatial coevolutionary dynamics in population games with environmental feedbacks

Feedback between game strategies and environmental states is common in human-natural systems. Existing studies have reported several interesting dynamical behaviors by studying the impact of environmental state on strategy selection. In this paper we construct a characterization of environmental states, assuming that environmental states are determined by local and global environmental states. Based on this we construct a spatial multiagent coevolutionary model to describe the strategy evolution of populations and analyze the model's dynamics by means of Monte Carlo simulations and mean-field approximation. We find that spatial structure can enhance the system stability, preventing the emergence of complex dynamical behaviors such as chaos. Furthermore, we incorporate a diffusion mechanism into the model. Results show that resource diffusion accelerates strategy switching by weakening differences in local environmental states. Numerical results further indicate that spatial structure significantly affects the system stability: the system self-organizes into stable spatial structures analogous to Turing patterns, thus enhancing the system stability. This study investigates the mechanisms by which environmental states and spatial structures influence system stability, offering new insights into understanding the coevolutionary dynamics in real-world systems.