IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/23742.html
   My bibliography  Save this paper

A Differential game approach in the case of a polluting oligopoly

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/23742/1/MPRA_paper_23742.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Kenji Fujiwara & Norimichi Matsueda, 2007. "On a Nonlinear Feedback Strategy Equilibrium of a Dynamic Game," Economics Bulletin, AccessEcon, vol. 3(8), pages 1-10.
    3. repec:ebl:ecbull:v:3:y:2007:i:8:p:1-10 is not listed on IDEAS
    4. 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.
    5. Kirman, Alan P & Sobel, Matthew J, 1974. "Dynamic Oligopoly with Inventories," Econometrica, Econometric Society, vol. 42(2), pages 279-287, March.
    6. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    7. Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
    8. 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.
    9. repec:dau:papers:123456789/1024 is not listed on IDEAS
    10. 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.
    11. 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.
    12. 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.
    13. Christopher Harris & John Vickers, 1987. "Racing with Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 1-21.
    14. Szidarovszky, Ferenc & Yen, Jerome, 1995. "Dynamic Cournot oligopolies with production adjustment costs," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 95-101.
    15. 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.
    16. 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.
    17. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    18. 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.
    19. Benabou, Roland, 1989. "Optimal Price Dynamics and Speculation with a Storable Good," Econometrica, Econometric Society, vol. 57(1), pages 41-80, January.
    20. Haucap, Justus & Kirstein, Roland, 2003. "Government Incentives When Pollution Permits Are Durable Goods," Public Choice, Springer, vol. 115(1-2), pages 163-183, April.
    21. 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.
    22. 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.
    23. Carlier, G., 2008. "Differentiability properties of rank-linear utilities," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 15-23, January.
    24. L. Lambertini, 2007. "Volatility forecasting for crude oil futures," Working Papers 598, Dipartimento Scienze Economiche, Universita' di Bologna.
    25. 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.
    26. 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, January.
    27. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bård Harstad, 2016. "The Dynamics of Climate Agreements," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 719-752.
    2. Santiago J. Rubio, 2002. "On The Coincidence Of The Feedback Nash And Stackelberg Equilibria In Economic Applications Of Differential Games," Working Papers. Serie AD 2002-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.
    4. Caputo, Michael R. & Ling, Chen, 2013. "The intrinsic comparative dynamics of locally differentiable feedback Nash equilibria of autonomous and exponentially discounted infinite horizon differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1982-1994.
    5. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
    6. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    7. Doraszelski, Ulrich & Escobar, Juan F., 2019. "Protocol invariance and the timing of decisions in dynamic games," Theoretical Economics, Econometric Society, vol. 14(2), May.
    8. Halkos, George, 2010. "Dynamic regulations in non –renewable resources oligopolistic markets," MPRA Paper 24774, University Library of Munich, Germany.
    9. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
    10. Zaruhi Hakobyan & Christos Koulovatianos, 2021. "Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth," Dynamic Games and Applications, Springer, vol. 11(1), pages 54-83, March.
    11. Eggert, Wolfgang & Itaya, Jun-ichi & Mino, Kazuo, 2011. "A dynamic model of conflict and appropriation," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 167-182.
    12. Luca Lambertini, 2016. "Managerial Delegation in a Dynamic Renewable Resource Oligopoly," Dynamic Modeling and Econometrics in Economics and Finance, in: Herbert Dawid & Karl F. Doerner & Gustav Feichtinger & Peter M. Kort & Andrea Seidl (ed.), Dynamic Perspectives on Managerial Decision Making, pages 93-107, Springer.
    13. Akihiko Yanase, 2009. "Global environment and dynamic games of environmental policy in an international duopoly," Journal of Economics, Springer, vol. 97(2), pages 121-140, June.
    14. Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
    15. Calvo, Emilio & Rubio, Santiago J., 2013. "Dynamic Models of International Environmental Agreements: A Differential Game Approach," International Review of Environmental and Resource Economics, now publishers, vol. 6(4), pages 289-339, April.
    16. Lambertini, Luca, 2021. "Regulating the tragedy of commons: Nonlinear feedback solutions of a differential game with a dual interpretation," Energy Economics, Elsevier, vol. 100(C).
    17. 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.
    18. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    19. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    20. Dubovik, Andrei & Parakhonyak, Alexei, 2014. "Drugs, guns, and targeted competition," Games and Economic Behavior, Elsevier, vol. 87(C), pages 497-507.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:23742. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.