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