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We analyze a differential game with spatially distributed controls to study amultiregional transboundary pollution problem. The dynamics of the statevariable (pollution stock) is defined by a two dimensional parabolic partialdifferential equation. The control variables (emissions) are spatiallydistributed variables. The model allows for a, possibly large, number of agentswith predetermined geographical relationships. For a special functional formpreviously used in the literature of transboundary pollution dynamic games weanalytically characterize the feedback Nash equilibrium. We show that at theequilibrium both the level and the location of emissions of each region dependon the particular geographical relationship among agents. We prove that, evenin a simplified model, the geographical considerations can modify the players'optimal strategies and therefore, the spatial aspects of the model should notbe overlooked.

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