Journal of Optimization Theory and Applications

, Volume 163, Issue 2, pp 642–659 | Cite as

A Differential Game of Transboundary Industrial Pollution with Emission Permits Trading

  • Shoude Li


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.


Differential game Emission permits trading HJB equation 



The author thanks the comments of the anonymous referees, the editor for careful reading and valuable comments on the first version of this paper, and Long Chen for his assistance in mathematical derivation and numerical analysis. Any remaining errors are my responsibility. This research was supported by the Philosophy and Social Science Foundation of Shanghai, China (Project No. 2012BJB002).


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Antai College of Economics and ManagementShanghai Jiao Tong UniversityShanghaiChina

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