Equilibrium strategies in a multiregional transboundary pollution differential game with spatially distributed controls

We analyze a differential game with spatially distributed controls to study multiregional transboundary pollution problem. The dynamics of the state variable (pollution stock) is defined by two dimensional parabolic partial equation. control variables (emissions) are variables. model allows for a, possibly large, number agents predetermined geographical relationships. For special functional form previously used in literature dynamic games we analytically characterize feedback Nash equilibrium. show that at equilibrium both level and location emissions each region depend on particular relationship among agents. prove that, even simplified model, considerations can modify players' optimal strategies therefore, spatial aspects should not be overlooked.