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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Segerson, Kathleen, 1988. "Uncertainty and incentives for nonpoint pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 15(1), pages 87-98, March.
    3. 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.
    4. 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.
    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.
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