Transboundary air pollution arises from inherently coupled, nonlinear dynamical processes that evolve across political borders and generate complex feedbacks between environmental quality, economic activity, and strategic behaviour. Bilateral trade, while strengthening economic interdependence, introduces additional feedback loops and control conflicts that can destabilize coordinated pollution management. Consequently, designing effective regulatory interventions in trade-dependent regions remains a persistent challenge. In this study, we formulate a two-country nonlinear differential game in which each nation regulates a shared pollution stock while simultaneously engaging in bilateral trade. The pollution dynamics and welfare functions form an interconnected controlled dynamical system, and we derive feedback Nash equilibrium strategies under both cooperative and non-cooperative regimes. Using the Hamilton–Jacobi–Bellman (HJB) framework, we obtain optimal control laws governing abatement efforts and characterize how the presence or absence of trade reshapes each country’s optimal dynamic response. Through numerical simulations of the resulting equilibria under varying trade intensities and abatement efficiencies, we uncover a nontrivial dynamic pattern: non-cooperative strategies can transiently yield higher welfare due to short-term economic gains, but they also amplify pollution accumulation and destabilize long-run system trajectories. In contrast, cooperative feedback controls consistently drive the system toward lower pollution stocks, improved long-term welfare stability, and more robust equilibrium behaviour. These findings underscore the importance of viewing transboundary pollution management as a controlled nonlinear dynamical system, where coordination acts as a stabilizing mechanism that reshapes both environmental and economic outcomes.
Kumar et al. (Wed,) studied this question.