A differential game of transboundary industrial pollution with emission permits trading. (English) Zbl 1302.91163

Summary: 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 D. W. K. Yeung [J. Optim. Theory Appl. 134, No. 1, 143–160 (2007; Zbl 1210.91098)]. 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.


91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
49N70 Differential games and control
49N90 Applications of optimal control and differential games
49L20 Dynamic programming in optimal control and differential games
91A23 Differential games (aspects of game theory)
91A10 Noncooperative games
91A12 Cooperative games


Zbl 1210.91098
Full Text: DOI


[1] Kaitala, V.; Pohjola, M.; Tahvonen, O., Transboundary air pollution and soil acidification: a dynamic analysis of an acid rain game between Finland and the USSR, Environ. Resour. Econ., 2, 161-181, (1992)
[2] Kaitala, V.; Pohjola, M.; Tahvonen, O., An economic analysis of transboundary air pollution between Finland and the soviet union, Scand. J. Econ., 94, 409-424, (1992)
[3] Long, N.V., Pollution control: a differential game approach, Ann. Oper. Res., 37, 283-296, (1992) · Zbl 0802.90141
[4] Ploeg, F.; Zeeuw, A.J., International aspects of pollution control, Environ. Resour. Econ., 2, 117-139, (1992)
[5] Dockner, E.J.; Long, N.V., International pollution control: cooperative versus noncooperative strategies, J. Environ. Econ. Manag., 25, 13-29, (1993) · Zbl 0775.90309
[6] Zagonari, F., International pollution problems: unilateral initiatives by environmental groups in one country, J. Environ. Econ. Manag., 36, 46-69, (1998) · Zbl 0914.90065
[7] Martin, W.E.; Patrick, R.H.; Tolwinski, B., A dynamic game of a transboundary pollutant with asymmetric players, J. Environ. Econ. Manag., 24, 1-12, (1993) · Zbl 0775.90311
[8] Hoel, M.; Pethig, R. (ed.), Emission taxes in a dynamic international game of CO_{2} emissions, (1992), Berlin
[9] Hoel, M., Intertemporal properties of an international carbon tax, Resour. Energy Econ., 15, 51-70, (1993)
[10] Dockner, E.; Long, N.V.; Sorger, G., Analysis of Nash equilibria in a class of capital accumulation games, J. Econ. Dyn. Control, 20, 1209-1235, (1996) · Zbl 0875.90352
[11] Maler, K.G.; Zeeuw, A., The acid rain differential game, Environ. Resour. Econ., 12, 167-184, (1998)
[12] List, J.A.; Mason, C.F., Optimal institutional arrangements for transboundary pollutants in a second-best world: evidence from a differential game with asymmetric players, J. Environ. Econ. Manag., 42, 277-296, (2001) · Zbl 1050.91018
[13] Yanase, A., Pollution control in open economies: implications of within-period interactions for dynamic game equilibrium, J. Econ., 84, 277-311, (2005) · Zbl 1122.91059
[14] Dutta, P.K.; Radner, R., Population growth and technological change in a global warming model, Econ. Theory, 29, 251-270, (2006) · Zbl 1117.91015
[15] Dutta, P.K.; Radner, R., Strategic analysis of global warming: theory and some numbers, J. Econ. Behav. Organ., 71, 187-209, (2009)
[16] Yeung, D.W.K., Dynamically consistent cooperative solution in a differential game of transboundary industrial pollution, J. Optim. Theory Appl., 134, 143-160, (2007) · Zbl 1210.91098
[17] Yeung, D.W.K.; Petrosyan, L.A., A cooperative stochastic differential game of transboundary industrial pollution, Automatica, 44, 1532-1544, (2008) · Zbl 1283.93324
[18] Forster, B., Optimal consumption planning in a polluted environment, J. Environ. Econ. Manag., 2, 1-6, (1973) · Zbl 0312.90015
[19] Breton, M.; Zaccour, G.; Zahaf, M., A differential game of joint implementation of environmental projects, Automatica, 41, 1737-1749, (2005) · Zbl 1125.91309
[20] Breton, M.; Martin-Herran, G., Equilibrium investment strategies in foreign environmental projects, J. Optim. Theory Appl., 130, 23-40, (2006) · Zbl 1139.91011
[21] Jørgensen, S.; Zaccour, G., Incentive equilibrium strategies and welfare allocation in a dynamic game of pollution control, Automatica, 37, 29-36, (2001) · Zbl 1038.91509
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.