  Motivated by the climate crisis that is currently ravaging the planet, we
propose and analyze a novel framework for the evolution of anthropogenic
climate impact in which the evolution of human environmental behavior and
environmental impact is coupled. Our framework includes a human decision-making
process that captures social influence, government policy interventions, and
the cost of environmentally-friendly behavior, modeled within a game-theoretic
paradigm. By taking a mean-field approach in the limit of large populations, we
derive the equilibria and their local stability characteristics. Subsequently,
we study global convergence, whereby we show that the system converges to a
periodic solution for almost all initial conditions. Numerical simulations
confirm our findings and suggest that, before the system reaches such a
periodic solution, the level of environmental impact might become dangerously
high, calling for the design of optimal control strategies to influence the
system trajectory.
