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Feedback Nash equilibria for non-linear differential games in pollution control

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  • Kossioris, G.
  • Plexousakis, M.
  • Xepapadeas, A.
  • de Zeeuw, A.
  • Mäler, K.-G.

Abstract

Dynamic problems of pollution and resource management with stock externalities often require a differential games framework of analysis. In addition they are represented realistically by non-linear transition equations. However, feedback Nash equilibrium (FBNE) solutions, which are the desired ones in this case, are difficult to obtain in problems with non-linear-quadratic structure. We develop a method to obtain numerically non-linear FBNE for a class of such problems, with a specific example for shallow lake pollution control. We compare FBNE solutions, by considering the entire equilibrium trajectories, with optimal management and open-loop solutions, and we show that the value of the best FBNE is in general worse than the open-loop and optimal management solutions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 32 (2008)
Issue (Month): 4 (April)
Pages: 1312-1331

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Handle: RePEc:eee:dyncon:v:32:y:2008:i:4:p:1312-1331

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References

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  1. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
  2. Dockner, E.J. & Wagener, F.O.O., 2006. "Markov-Perfect Nash Equilibria in Models With a Single Capital Stock," CeNDEF Working Papers 06-07, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  3. Hein, Lars, 2006. "Cost-efficient eutrophication control in a shallow lake ecosystem subject to two steady states," Ecological Economics, Elsevier, vol. 59(4), pages 429-439, October.
  4. W.A. Brock & D. Starrett, 2003. "Managing Systems with Non-convex Positive Feedback," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 575-602, December.
  5. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, vol. 24(3), pages 251-261, June.
  6. Ploeg, F. van der & Zeeuw, A.J. de, 1990. "International aspects of pollution control," Discussion Paper 1990-65, Tilburg University, Center for Economic Research.
  7. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
  8. Mäler, K-G. & Xepapadeas, A. & Zeeuw, A.J. de, 2003. "The economics of shallow lakes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123314, Tilburg University.
  9. Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
  10. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
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Citations

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Cited by:
  1. XEPAPADEAS, Anastasios, 2009. "Modeling Complex Systems," MPRA Paper 17498, University Library of Munich, Germany.
  2. Athanassoglou, Stergios, 2010. "Dynamic nonpoint-source pollution control policy: Ambient transfers and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2494-2509, December.
  3. Talat S. Genc & Georges Zaccour, 2010. "Investment Dynamics: Good News Principle," Working Papers 1006, University of Guelph, Department of Economics and Finance.
  4. Anne-Sophie Crépin & Therese Lindahl, 2009. "Grazing Games: Sharing Common Property Resources with Complex Dynamics," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 44(1), pages 29-46, September.
  5. F.O.O. Wagener, 2009. "Shallow Lake Economics Run Deep: Nonlinear Aspects of an Economic-Ecological Interest Conflict," Tinbergen Institute Discussion Papers 09-033/1, Tinbergen Institute.
  6. Engelbert J. Dockner & Florian O.O. Wagener, 2006. "Markov-Perfect Nash Equilibria in Models with a Single Capital Stock," Tinbergen Institute Discussion Papers 06-055/1, Tinbergen Institute.
  7. Salerno, Gillian & Beard, Rodney & McDonald, Stuart, 2007. "Rent Seeking Behavior and Optimal Taxation of Pollution in Shallow Lakes," MPRA Paper 11225, University Library of Munich, Germany, revised 22 Oct 2008.
  8. Pedro, de Mendonça, 2009. "Self-Enforcing Climate Change Treaties: A Generalized Differential Game Approach with Applications," MPRA Paper 17889, University Library of Munich, Germany.
  9. George Kossioris & Michael Plexousakis & Anastasios Xepapadeas & Aart de Zeeuw, . "On the Optimal Taxation of Common-Pool Resources," DEOS Working Papers 1010, Athens University of Economics and Business.
  10. Heijnen, P. & Wagener, F.O.O., 2013. "Avoiding an ecological regime shift is sound economic policy," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1322-1341.
  11. Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.
  12. Anastasios Xepapadeas, . "The Economics of Nonpoint Source Pollution," DEOS Working Papers 1233, Athens University of Economics and Business.

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