  We analyze 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.
