Cooperation in pollution control problems via evolutionary variational inequalities

In this paper, we develop a cooperative game framework for modeling the pollution control problem in a time-dependent setting. We examine the situation in which different countries, aiming at reducing pollution emissions, coordinate both emissions and investment strategies to optimize jointly their welfare. We state the equilibrium conditions underlying the model and provide a formulation in terms of an evolutionary variational inequality. Then, by means of infinite dimensional duality tools, we prove the existence of Lagrange multipliers that play a fundamental role to describe countries' decision-making processes. Finally, we discuss the existence of solutions and provide a numerical example.