Viable Nash equilibrium in the problem of common pollution
Abstract
Two countries produce goods and are penalized by the common pollution they generate. Each country maximizes an inter-temporal utility criterion, taking account of the pollution stock to which both contribute. The dynamic is in continuous time with possible sudden switches to less polluting technologies. The set of Nash equilibria, for which solutions also remain in the set of constraints, is the intersection of two manifolds in a certain state space. At the Nash equilibrium, the choices of the two countries are interdependent: different productivity levels after switching lead the more productive country to hasten and the less productive to delay the switch. In the absence of cooperation, efforts by one country to pollute less motivate the other to pollute more, or encourage the country that will be cleaner or less productive country after switching to delay its transition.
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