IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v242y2026icp125-147.html

Dynamic stability of Stackelberg equilibrium in mixed oligopolies: The role of social responsibility, marginal costs, and market structure

Author

Listed:
  • Ren, Jing
  • Sun, Hao
  • Sun, Panfei

Abstract

This paper investigates how corporate social responsibility, marginal costs, and market structure affect the stability of the Stackelberg equilibrium in mixed oligopolies. To achieve this, we develop dynamic mixed duopoly and triopoly models, showing that the Stackelberg equilibrium is locally asymptotically stable when the adjustment speed is below a threshold. The stability of the equilibrium is enhanced by increased marginal costs, stronger commitment to social responsibility, and the presence of a sophisticated follower in the triopoly setting. However, when the adjustment speed exceeds the threshold and the equilibrium becomes unstable, we introduce a control term into the dynamic model to restore stability. The implications of our analysis highlight the importance of firms avoiding excessive cost cutting in favor of innovation driven competition. Additionally, fostering social responsibility and moderate market competition plays a critical role in sustaining stable markets over the long term.

Suggested Citation

  • Ren, Jing & Sun, Hao & Sun, Panfei, 2026. "Dynamic stability of Stackelberg equilibrium in mixed oligopolies: The role of social responsibility, marginal costs, and market structure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 242(C), pages 125-147.
    • Handle: RePEc:eee:matcom:v:242:y:2026:i:c:p:125-147
    DOI: 10.1016/j.matcom.2025.11.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542500477X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2025.11.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
    2. Luca Lambertini & Arsen Palestini & Alessandro Tampieri, 2016. "CSR in an Asymmetric Duopoly with Environmental Externality," Southern Economic Journal, Southern Economic Association, vol. 83(1), pages 236-252, July.
    3. Mai, Fengxia & Zhang, Jianxiong & Sun, Xiaojie, 2021. "Dynamic analysis of pricing model in a book supply chain," International Journal of Production Economics, Elsevier, vol. 233(C).
    4. Yu Yu & Weisheng Yu, 2019. "The Complexion of Multi-period Stackelberg Triopoly Game with Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 457-478, January.
    5. Andaluz, J. & Elsadany, A.A. & Jarne, G., 2023. "Dynamic behavior in a Cournot duopoly with social responsibility," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Chad Syverson, 2004. "Market Structure and Productivity: A Concrete Example," Journal of Political Economy, University of Chicago Press, vol. 112(6), pages 1181-1222, December.
    7. Atefeh Ahmadi & Sourav Roy & Mahtab Mehrabbeik & Dibakar Ghosh & Sajad Jafari & Matjaž Perc, 2023. "The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players," PLOS ONE, Public Library of Science, vol. 18(4), pages 1-22, April.
    8. Azioune, Mourad & Abdelouahab, Mohammed-Salah, 2025. "Controlling chaos and mixed mode oscillations in a Bertrand duopoly game with homogeneous expectations and quadratic cost functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 233(C), pages 553-566.
    9. Caroline Flammer, 2015. "Does Corporate Social Responsibility Lead to Superior Financial Performance? A Regression Discontinuity Approach," Management Science, INFORMS, vol. 61(11), pages 2549-2568, November.
    10. Tomáš Tichý & Davide Radi & Fabio Lamantia, 2022. "Hybrid evolutionary oligopolies and the dynamics of corporate social responsibility," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 87-114, January.
    11. Rui Albuquerque & Yrjö Koskinen & Chendi Zhang, 2019. "Corporate Social Responsibility and Firm Risk: Theory and Empirical Evidence," Management Science, INFORMS, vol. 65(10), pages 4451-4469, October.
    12. S. S. Askar, 2020. "Duopolistic Stackelberg game: investigation of complex dynamics and chaos control," Operational Research, Springer, vol. 20(3), pages 1685-1699, September.
    13. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    14. Lambertini, Luca & Tampieri, Alessandro, 2015. "Incentives, performance and desirability of socially responsible firms in a Cournot oligopoly," Economic Modelling, Elsevier, vol. 50(C), pages 40-48.
    15. Henri Servaes & Ane Tamayo, 2013. "The Impact of Corporate Social Responsibility on Firm Value: The Role of Customer Awareness," Management Science, INFORMS, vol. 59(5), pages 1045-1061, May.
    16. 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.
    17. Luca Lambertini & Arsen Palestini & Alessandro Tampieri, 2016. "CSR in an Asymmetric Duopoly with Environmental Externality," Southern Economic Journal, John Wiley & Sons, vol. 83(1), pages 236-252, July.
    18. Peng, Yu & Lu, Qian, 2015. "Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 259-268.
    19. Askar, S.S., 2022. "Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    20. Askar, S.S., 2022. "On the dynamics of Cournot duopoly game with private firms: Investigations and analysis," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    21. Wu, Ruijia & Van Gorder, Robert A., 2018. "Nonlinear dynamics of discrete time multi-level leader–follower games," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 240-250.
    22. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    23. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    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. Yan, Bo & Ahmadi, Atefeh & Mehrabbeik, Mahtab & Rajagopal, Karthikeyan & He, Shaobo & Jafari, Sajad, 2022. "Expanding the duopoly Stackelberg game with marginal costs into a multipoly game with lowering the burden of mathematical calculations: a numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Tian, Yi & Ma, Junhai & Xie, Lei & Koivumäki, Timo & Seppänen, Veikko, 2020. "Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Buccella, Domenico & Fanti, Luciano & Gori, Luca, 2024. "Corporate Social Responsibility: A theory of the firm revisited with environmental issues," GLO Discussion Paper Series 1421, Global Labor Organization (GLO).
    4. Yasuhiko Nakamura, 2023. "Corporate social responsibility and endogenous competition structure in an industry composed of firms with generalized biased managers," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(6), pages 3645-3665, September.
    5. Chang, Juin-Jen & Chen, Jhy-Hwa & Tsai, Ming-Fang, 2022. "Corporate social responsibility, social optimum, and the environment-growth tradeoff," Resource and Energy Economics, Elsevier, vol. 69(C).
    6. Ningning Wang & Zhuoxin Li, 2021. "Supplier Encroachment with a Dual‐Purpose Retailer," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2672-2688, August.
    7. Atefeh Ahmadi & Sourav Roy & Mahtab Mehrabbeik & Dibakar Ghosh & Sajad Jafari & Matjaž Perc, 2023. "The dynamics of a duopoly Stackelberg game with marginal costs among heterogeneous players," PLOS ONE, Public Library of Science, vol. 18(4), pages 1-22, April.
    8. Kai Zhang & Xubei Lian & Leonard F. S. Wang, 2024. "Green finance, loan commitment, and environmental corporate social responsibility in a differentiated duopoly," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 45(1), pages 394-413, January.
    9. Lisa Planer-Friedrich & Marco Sahm, 2020. "Strategic corporate social responsibility, imperfect competition, and market concentration," Journal of Economics, Springer, vol. 129(1), pages 79-101, January.
    10. Tian, Huaigu & Wang, Zhen & Zhang, Peijun & Li, Jianhui & Wang, Qiao & Zhang, Shaohua, 2026. "Complex dynamics of a symmetric quantum Stackelberg duopoly game model with heterogeneous expectations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
    11. 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.
    12. Sun, Zeyu & Li, Xiaohui & Xie, Jing & Cheng, C.S., 2023. "How does dividend payout affect corporate social responsibility? A channel analysis," Journal of Financial Stability, Elsevier, vol. 68(C).
    13. Angelidis, Timotheos & Michairinas, Athanasios & Sakkas, Athanasios, 2024. "World ESG performance and economic activity," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 93(C).
    14. Shackleton, Mark & Yan, Jiali & Yao, Yaqiong, 2022. "What drives a firm's ES performance? Evidence from stock returns," Journal of Banking & Finance, Elsevier, vol. 136(C).
    15. Stefano Clo' & Gianluca Iannucci & Alessandro Tampieri, 2024. "Emission permits and firms' environmental responsibility," Working Papers - Economics wp2024_06.rdf, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    16. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    17. Tamas Barko & Martijn Cremers & Luc Renneboog, 2022. "Shareholder Engagement on Environmental, Social, and Governance Performance," Journal of Business Ethics, Springer, vol. 180(2), pages 777-812, October.
    18. Gillan, Stuart L. & Koch, Andrew & Starks, Laura T., 2021. "Firms and social responsibility: A review of ESG and CSR research in corporate finance," Journal of Corporate Finance, Elsevier, vol. 66(C).
    19. Biancardi, Marta & Iannucci, Gianluca & Villani, Giovanni, 2024. "Water dynamics and environmental social practice in a differential game," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    20. Galinato, Gregmar I. & Hyland, Marie & Islam, Asif M., 2022. "Does corporate social responsibility benefit society? Evidence from Latin America," Emerging Markets Review, Elsevier, vol. 53(C).

    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:eee:matcom:v:242:y:2026:i:c:p:125-147. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.