A Differential Game of Transboundary Industrial Pollution with Emission Permits Trading

Transboundary pollution is a particularly serious problem as it leads people located at regional borders to disproportionately suffer from pollution. In 2007, a cooperative differential game model of transboundary industrial pollution was presented by Yeung. It is the first time that time-consistent solutions are derived in a cooperative differential game on pollution control with industries and governments being separate entities. In this paper, we extend Yeung's model to an even more general model, in which emission permits trading is taken into account. Our objective is to make use of optimal control theory to find the two regions' noncooperative and cooperative optimal emission paths such that the regions' discounted stream of net revenues is maximized. We illustrate the results with a numerical example.