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The Acid Rain Differential Game


  • Karl-Göran Mäler
  • Aart De Zeeuw



This paper considers an acid rain differential game. Countries emit sulphur which is partly transferred to other countries. Depositions above critical loads ultimately destroy the soil. Countries face a trade-off between the costs of emission reductions and the damage to the soil due to the depletion of the acid buffers. Because of the transboundary externalities the outcome will depend on whether the countries cooperate or not. This paper presents the cooperative outcome and the open-loop and Markov-perfect Nash equilibria of the acid rain differential game. It will be shown that the depositions always converge to the critical loads but the steady-state levels of the buffer stocks differ. The theory is used to analyse the acid rain differential game for sulphur between Great Britain and Ireland. Finally, some results are given for the whole of Europe. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Karl-Göran Mäler & Aart De Zeeuw, 1998. "The Acid Rain Differential Game," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 12(2), pages 167-184, September.
  • Handle: RePEc:kap:enreec:v:12:y:1998:i:2:p:167-184
    DOI: 10.1023/A:1008273509255

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    References listed on IDEAS

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    2. Charles F Mason, 2017. "Climate Change and Migration: A Dynamic Model," CESifo Economic Studies, CESifo, vol. 63(4), pages 421-444.
    3. GERMAIN, Marc & TOINT, Philippe & TULKENS, Henry & DE ZEEUW, Aart, 1998. "Transfers to sustain core-theoretic cooperation in international stock pollutant control," CORE Discussion Papers 1998032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Javier de Frutos & Guiomar Martín-Herrán, 2016. "Pollution control in a multiregional setting: a differential game with spatially distributed controls," Gecomplexity Discussion Paper Series 201601, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Jan 2016.
    5. Francisco Alvarez-Cuadrado & Ngo Van Long, 2008. "Relative Consumption and Resource Extraction," CIRANO Working Papers 2008s-27, CIRANO.
    6. Claudio Piga, 2003. "Pigouvian Taxation in Tourism," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(3), pages 343-359, November.
    7. GERMAIN, Marc & VAN YPERSELE, Jean-Pascal, 1999. "Financial transfers to sustain international cooperation in the climate change framework," CORE Discussion Papers 1999036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Mason, Charles F. & Polasky, Stephen & Tarui, Nori, 2017. "Cooperation on climate-change mitigation," European Economic Review, Elsevier, vol. 99(C), pages 43-55.
    9. Iho, Antti & Parker, Doug & Zilberman, David, 2013. "Optimal Regional Policies to Control Manure Nutrients to Surface and Ground Waters," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149922, Agricultural and Applied Economics Association.
    10. Fernandez, Linda, 2002. "Trade's Dynamic Solutions to Transboundary Pollution," Journal of Environmental Economics and Management, Elsevier, vol. 43(3), pages 386-411, May.
    11. Iho, Antti, 2013. "Optimal Regional Policies to Control Manure Nutrients to Surface and GroundWaters," 87th Annual Conference, April 8-10, 2013, Warwick University, Coventry, UK 158683, Agricultural Economics Society.
    12. Santiago J. Rubio, 2001. "International Cooperation In Pollution Control," Working Papers. Serie AD 2001-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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    15. Kristen A. Sheeran, 2006. "Side Payments of Exceptions: The Implications for Equitable and Efficient Climate Control," Eastern Economic Journal, Eastern Economic Association, vol. 32(3), pages 515-532, Summer.
    16. Schmieman, Erik C. & van Ierland, Ekko C., 1999. "Dynamics of soil acidification: an economic analysis," Ecological Economics, Elsevier, vol. 31(3), pages 449-462, December.
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    19. van den Broek, W. A., 2002. "Moving horizon control in dynamic games," Journal of Economic Dynamics and Control, Elsevier, vol. 26(6), pages 937-961, June.
    20. Charles F. Mason, 2017. "Transboundary Externalities and Reciprocal Taxes: A Differential Game Approach," CESifo Working Paper Series 6561, CESifo Group Munich.
    21. Finus, Michael & Tjotta, Sigve, 2003. "The Oslo Protocol on sulfur reduction: the great leap forward?," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 2031-2048, September.
    22. Müller-Fürstenberger, Georg & Schumacher, Ingmar, 2017. "The consequences of a one-sided externality in a dynamic, two-agent framework," European Journal of Operational Research, Elsevier, vol. 257(1), pages 310-322.
    23. Hennessy, David A., 2008. "Biosecurity incentives, network effects, and entry of a rapidly spreading pest," Ecological Economics, Elsevier, vol. 68(1-2), pages 230-239, December.
    24. Ansuategi, Alberto & Escapa, Marta, 2002. "Economic growth and greenhouse gas emissions," Ecological Economics, Elsevier, vol. 40(1), pages 23-37, January.
    25. Erik Schmieman & Ekko van Ierland & Leen Hordijk, 2002. "Dynamic Efficiency with Multi-Pollutants and Multi-Targets The Case of Acidification and Tropospheric Ozone Formation in Europe," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 23(2), pages 133-148, October.

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    acid rain; critical loads; differential games;


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