A differential game analysis of multipollutant transboundary pollution in river basin

Abstract

In this paper, we present a differential game model of watershed multi-pollutant transboundary pollution in which the pollutants can be either technological substitutes or complements, and the abatement costs of two pollutants are not separable. It is the first time that the multi-pollutant is derived in a cooperative differential game on transboundary pollution control. The results are discussed with some illustrative examples under the cases of the pollutants are substitutes and complements. Our results show that (i) the system always admits saddle point steady-state equilibrium under the non-cooperative and cooperative games,respectively; (ii) when the pollutants are substitutes or complements, the upstream region optimal emission levels in the cooperative game are lower than that in the non-cooperative game; while the downstream region optimal emission levels in the cooperative game are equal to that in the non-cooperative game; (iii) the upstream region optimal pollution stocks in the cooperative game are lower than that in the non-cooperative game under the case when the pollutants are substitutes or complements.