Coevolutionary game dynamics with localized environmental resource feedback

TL;DR

This paper explores how spatial heterogeneity and feedback mechanisms in environmental resources influence coevolutionary dynamics in prisoner's dilemma games, revealing conditions that prevent oscillatory tragedies and promote stable cooperation.

Contribution

It introduces a spatially heterogeneous resource model with feedback in evolutionary games, highlighting how high influence of strategies on resources can stabilize cooperation.

Findings

Oscillatory tragedy of the commons can be avoided with high strategy-resource influence.

Self-organized clustered patterns emerge in lattice simulations, enhancing stability.

Transition robustness across various parameters and initial conditions.

Abstract

Dynamic environments shape diverse dynamics in evolutionary game systems. We introduce spatial heterogeneity of resources into the prisoner's dilemma game model to explore coevolutionary game dynamics with environmental feedback. The availability of resources significantly affects the survival competitiveness of surrounding individuals. Feedback between individuals' strategies and the resources they can use leads to the oscillating dynamic known as the "oscillatory tragedy of the commons". Our findings indicate that when the influence of individuals' strategies on the update rate of resources is significantly high in systems characterized by environmental heterogeneity, they can attain an equilibrium state that avoids the oscillatory tragedy. In contrast to the numerical results obtained in well-mixed structures, self-organized clustered patterns emerge in simulations utilizing square lattices, further enhancing the stability of the system. We discuss critical phenomena in detail, demonstrating that the aforementioned transition is robust across various system parameters, including the strength of cooperators in restoring the environment, initial distributions of cooperators, system size and structures, and noise.