Mean Field Stackelberg Game for Production and Carbon Emission Reduction with State Reflections

Abstract: Global warming, driven by anthropogenic carbon emissions with transboundary pollution characteristics and irreversible damage, poses an existential threat to human society. This paper develops a novel two-level Stackelberg game with mean field interaction of controls and common noise which integrates hierarchical decision-making under a state-reflected emission dynamics. A central regulator (leader) adjusts product prices to guide $n$ heterogeneous competing regions (followers) while enforcing a hard emission cap via a reflection mechanism that models emergency reductions through a local time process. We establish the existence of an approximate Stackelberg equilibrium and perform sensitivity analysis via Monte Carlo simulations.