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.

我们分析了具有空间分布控制的差分博弈，以研究多区域跨界污染问题。状态变量（污染原液）的动力学由二维抛物线偏微分方程定义。控制变量（排放物）是空间分布的变量。该模型允许具有预定地理关系的可能很多的代理。对于先前在跨界污染动态博弈文献中使用的特殊功能形式，我们分析性地描述了反馈纳什均衡。我们表明，在平衡状态下，每个区域的排放水平和位置都取决于代理之间的特定地理关系。我们证明，即使在简化模型中，