Ensuring Mutual Benefit in a Trans-boundary Industrial Pollution Control Problem

Technological developments play a crucial role in allowing governments and industries to meet carbon emission targets, whilst maintaining cost effectiveness. Mathematical modeling related to climate change has often included technology (including technology transfer between nations) as an effective policy instrument. However, such models often incorporate technology as an exogenous variable, highlighting the need to further interrogate the role of technology, its dynamics and limitations on reducing international pollution levels to improve sustainability, energy reliability and subsequent policy initiatives. Hence, in this study, we consider technology as an endogenous variable within a broader trans-boundary industrial pollution problem with random interference factors to obtain a closed-loop (Markov perfect) Nash equilibrium. We then articulate the Nash non-cooperative and cooperative equilibria via a stochastic linear quadratic differential game paradigm and prove the stability of a cooperative game by using Pareto optimal solution. We show that under such strategies to control carbon pollution a cooperative game is more efficient than a non-cooperative game, emphasizing the importance of technology transfer and collaboration between nations, subsequently serving as a mutual benefit for multi-lateral efforts to reduce global carbon emissions. In doing so, our study highlights the role of government subsidy incentives when collaborating with industry to encourage the integration of carbon-reducing technologies, whilst simultaneously increasing each country’s net revenue. Hence, our study provides a novel insight and framework for policymakers when encouraging industry to use carbon capturing and storage technologies. We also emphasize that efforts to coordinate emissions control should be pursued jointly to ensure mutual benefit for government and industry alike.