IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i12p2007-d1681750.html
   My bibliography  Save this article

Emission Control in an n -Firm Oligopoly Game with Product Differentiation

Author

Listed:
  • Akio Matsumoto

    (Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji 192-0393, Tokyo, Japan
    Corvinus Institute for Advanced Studies, Corvinus University of Budapest, Fövám tér 8, 1093 Budapest, Hungary)

  • Ferenc Szidarovszky

    (Department of Mathematics, Corvinus University, Fövám tér 8, 1093 Budapest, Hungary
    Deceased author.)

Abstract

Is it possible to control NPS (non-point source) pollution whose sources, sizes, and origins are difficult to identify? This study provides a positive answer in a non-cooperative n -firm oligopoly model in which the firms determine levels of differentiated goods and abatement technologies. It first derives a Cournot–Nash equilibrium in which the firms maximize their profit and emit pollution under the ambient charge scheme, combining rewards from the total NPS concentration less than a given standard with the penalties above. The effect of the ambient charge is then analytically shown in homogeneous and heterogeneous duopoly and triopoly. Further, possible controllability is numerically examined in the case of n ≥ 4 .

Suggested Citation

  • Akio Matsumoto & Ferenc Szidarovszky, 2025. "Emission Control in an n -Firm Oligopoly Game with Product Differentiation," Mathematics, MDPI, vol. 13(12), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:2007-:d:1681750
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/12/2007/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/12/2007/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    2. Hideki Sato, 2017. "Pollution from Cournot duopoly industry and the effect of ambient charges," Journal of Environmental Economics and Policy, Taylor & Francis Journals, vol. 6(3), pages 305-308, July.
    3. Elias Asproudis & Eleftherios Filippiadis, 2021. "Environmental Technological Choice in a Cournot-Bertrand Model," Journal of Industry, Competition and Trade, Springer, vol. 21(1), pages 43-58, March.
    4. Segerson, Kathleen, 1988. "Uncertainty and incentives for nonpoint pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 15(1), pages 87-98, March.
    5. Akio Matsumoto & Ferenc Szidarovszky, 2025. "Optimal environmental policy for NPS pollution under random welfare," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 27(2), pages 139-167, April.
    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. Ahmad Naimzada & Marina Pireddu, 2023. "Differentiated goods in a dynamic Cournot duopoly with emission charges on output," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 305-318, June.
    2. Ohnishi, Kazuhiro, 2021. "The environmental effect of ambient charges in mixed triopoly with diverse firm objectives," MPRA Paper 108521, University Library of Munich, Germany.
    3. Ohnishi, Kazuhiro, 2024. "Pollution, partial privatization and the effect of ambient charges: price competition," MPRA Paper 120531, University Library of Munich, Germany.
    4. Ohnishi, Kazuhiro, 2021. "Pollution, partial privatization and the effect of ambient charges," MPRA Paper 109592, University Library of Munich, Germany, revised 04 Sep 2021.
    5. Akio Matsumoto & Ferenc Szidarovszky, 2025. "Optimal environmental policy for NPS pollution under random welfare," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 27(2), pages 139-167, April.
    6. Akio Matsumoto & Ferenc Szidarovszky, 2021. "Controlling non-point source pollution in Cournot oligopolies with hyperbolic demand," SN Business & Economics, Springer, vol. 1(2), pages 1-15, February.
    7. Ahmad Naimzada & Marina Pireddu, 2023. "Dynamic approaches for the evaluation of the environmental policy efficacy in a nonlinear Cournot duopoly with differentiated goods and emission charges," Working Papers 517, University of Milano-Bicocca, Department of Economics.
    8. Michael Kopel & Eva Maria Putz, 2021. "Information sharing in a Cournot–Bertrand duopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(7), pages 1645-1655, October.
    9. Ahmad Naimzada & Marina Pireddu, 2021. "On the detrimental effects of concave emission charges in a dynamic Cournot duopoly model," Working Papers 466, University of Milano-Bicocca, Department of Economics.
    10. Qiu, Zeyuan & Prato, Anthony A., 1999. "Accounting For Spatial Characteristics Of Watersheds In Evaluating Water Pollution Abatement Policies," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 31(01), pages 1-15, April.
    11. Frans P. Vries & Nick Hanley, 2016. "Incentive-Based Policy Design for Pollution Control and Biodiversity Conservation: A Review," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 63(4), pages 687-702, April.
    12. Armin Schmutzler, 1996. "Pollution control with imperfectly observable emissions," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 7(3), pages 251-262, April.
    13. Krzysztof Kosiec, 2016. "Liberalisation of International Trade – The Case of Asymmetric Countries," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 8(3), pages 143-160, September.
    14. Markus Reisinger & Ludwig Ressner, 2006. "The Choice of Prices vs. Quantities under Uncertainty," Working Papers 007, Bavarian Graduate Program in Economics (BGPE).
    15. Emmanuel Petrakis & Panagiotis Skartados, 2022. "Vertical Opportunism, Bargaining, and Share-Based Agreements," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 60(4), pages 549-565, June.
    16. Espínola-Arredondo, Ana & Muñoz-García, Félix, 2013. "When does environmental regulation facilitate entry-deterring practices," Journal of Environmental Economics and Management, Elsevier, vol. 65(1), pages 133-152.
    17. Lambertini, Luca, 1997. "Prisoners' Dilemma in Duopoly (Super)Games," Journal of Economic Theory, Elsevier, vol. 77(1), pages 181-191, November.
    18. Arijit Mukherjee & Burcu Senalp, 2024. "Complementary inputs, outsourcing and vertical integration: Price versus quantity competition," Manchester School, University of Manchester, vol. 92(5), pages 578-611, September.
    19. Aseem Kaul & Jiao Luo, 2018. "An economic case for CSR: The comparative efficiency of for‐profit firms in meeting consumer demand for social goods," Strategic Management Journal, Wiley Blackwell, vol. 39(6), pages 1650-1677, June.
    20. Bernhofen, Daniel M. & Bernhofen, Laura T., 1999. "On the likelihood of a prisoners' dilemma in a differentiated duopoly," Economics Letters, Elsevier, vol. 64(3), pages 291-294, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:gam:jmathe:v:13:y:2025:i:12:p:2007-:d:1681750. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.