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A Differential game approach in the case of a polluting oligopoly

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  • Halkos, George

Abstract

In this paper we propose an oligopolistic market model of pollution, where demand is not linear and firms are revenue maximizers. Additionally we assume that the rate of purification is very small tending to zero and that each firm accumulates a pollution share depending for example on firm’s size. The game ends up with Markov strategies employed by all firms. Our findings show that under conditions it is possible a marginal decrease on the total pollution stock to increase firms’ discounted revenues. A reallocation caused by a uniform decrease in all firms pollution, reorders the marginal change of the pollution stocks in reverse of the original order of the allowed pollution.

Suggested Citation

  • Halkos, George, 2009. "A Differential game approach in the case of a polluting oligopoly," MPRA Paper 23742, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:23742
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    References listed on IDEAS

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    1. Maskin, Eric & Tirole, Jean, 1987. "A theory of dynamic oligopoly, III : Cournot competition," European Economic Review, Elsevier, vol. 31(4), pages 947-968, June.
    2. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    3. Sundaram, Rangarajan K., 1989. "Perfect equilibrium in non-randomized strategies in a class of symmetric dynamic games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 153-177, February.
    4. Kenji Fujiwara & Norimichi Matsueda, 2007. "On a Nonlinear Feedback Strategy Equilibrium of a Dynamic Game," Economics Bulletin, AccessEcon, vol. 3(8), pages 1-10.
    5. repec:ebl:ecbull:v:3:y:2007:i:8:p:1-10 is not listed on IDEAS
    6. 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.
    7. Kirman, Alan P & Sobel, Matthew J, 1974. "Dynamic Oligopoly with Inventories," Econometrica, Econometric Society, vol. 42(2), pages 279-287, March.
    8. Benabou, Roland, 1989. "Optimal Price Dynamics and Speculation with a Storable Good," Econometrica, Econometric Society, vol. 57(1), pages 41-80, January.
    9. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    10. Haucap, Justus & Kirstein, Roland, 2003. "Government Incentives When Pollution Permits Are Durable Goods," Public Choice, Springer, vol. 115(1-2), pages 163-183, April.
    11. L. Lambertini, 2010. "Oligopoly with Hyperbolic Demand: A Differential Game Approach," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 108-119, April.
    12. Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
    13. Dockner, Engelbert J. & Van Long, Ngo & Sorger, Gerhard, 1996. "Analysis of Nash equilibria in a class of capital accumulation games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1209-1235.
    14. Stanisław Bylka & Stanisław Ambroszkiewicz & Jan Komar, 2000. "Discrete time dynamic game model for price competition in an oligopoly," Annals of Operations Research, Springer, vol. 97(1), pages 69-89, December.
    15. repec:dau:papers:123456789/1024 is not listed on IDEAS
    16. Fudenberg, Drew & Tirole, Jean, 1983. "Capital as a commitment: Strategic investment to deter mobility," Journal of Economic Theory, Elsevier, vol. 31(2), pages 227-250, December.
    17. Steffen Huck & Hans-Theo Normann & Jörg Oechssler, 2002. "Stability of the Cournot process - experimental evidence," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 123-136.
    18. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
    19. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    20. Carlier, G., 2008. "Differentiability properties of rank-linear utilities," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 15-23, January.
    21. L. Lambertini, 2007. "Volatility forecasting for crude oil futures," Working Papers 598, Dipartimento Scienze Economiche, Universita' di Bologna.
    22. Szidarovszky, Ferenc & Yen, Jerome, 1995. "Dynamic Cournot oligopolies with production adjustment costs," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 95-101.
    23. Howroyd, T. D. & Russell, A. M., 1984. "Cournot oligopoly models with time delays," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 97-103, October.
    24. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    25. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, I: Overview and Quantity Competition with Large Fixed Costs," Econometrica, Econometric Society, vol. 56(3), pages 549-569, May.
    26. Bernheim, B. Douglas & Ray, Debraj, 1989. "Markov perfect equilibria in altruistic growth economies with production uncertainty," Journal of Economic Theory, Elsevier, vol. 47(1), pages 195-202, February.
    27. 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.
    28. Wirl, Franz, 1996. "Can Leviathan Governments Mitigate the Tragedy of the Commons?," Public Choice, Springer, vol. 87(3-4), pages 363-377, June.
    29. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
    30. Van Cayseele, Patrick & Furth, Dave, 1996. "Bertrand-Edgeworth Duopoly with Buyouts or First Refusal Contracts," Games and Economic Behavior, Elsevier, vol. 16(2), pages 153-180, October.
    31. Eric Maskin & Jean Tirole, 1985. "A Theory of Dynamic Oligopoly, II: Price Competition," Working papers 373, Massachusetts Institute of Technology (MIT), Department of Economics.
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    More about this item

    Keywords

    Non linear strategies; Markov equilibrium; allowed pollution stock.;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • Q58 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Environmental Economics: Government Policy

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