The impact of dynamic compensation on coupled socio-ecological public goods game

Regarding the issue of protecting ecological resources, this paper establishes a coupled socio-ecological public goods game model to study the impact of dynamic compensation on individual behavior choices and resource evolution. When the compensation intensity is constant, it is found that there is an optimal compensation intensity under different enhancement factors, and the optimal value is negatively correlated with the enhancement factor. The results of the dynamic changes in the compensation intensity indicate that the system has two evolutionary processes: convergence to a stable value and periodic oscillation. Within the steady-state parameter range, a relatively small or large initial compensation intensity can lead the system to a highly vulnerable evolutionary path. Conversely, if sufficient compensation is provided to cooperators at the initial stage, the system will rapidly converge to the stable state of full cooperation. When the initial compensation intensity is moderate, cooperators and defectors coexist. Meanwhile, the greater the enhancement-degradation ratio for compensation intensity, the higher the level of cooperation. In addition, it tends to trigger more significant but slower fluctuations when the response speed of the compensation intensity to the group behavior is relatively slow, whereas a faster response speed leads to higher-frequency fluctuations. Within the parameter range where the system exhibits periodic oscillation, increasing the enhancement-degradation ratio for compensation intensity or the response speed of compensation intensity to group behavior will amplify the amplitude of the system, which is not conducive to the stability of the socio-ecological system.