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On the Oscillations in Cournot Games with Best Response Strategies

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  • Zhengyang Liu
  • Haolin Lu
  • Liang Shan
  • Zihe Wang

Abstract

In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model.

Suggested Citation

  • Zhengyang Liu & Haolin Lu & Liang Shan & Zihe Wang, 2024. "On the Oscillations in Cournot Games with Best Response Strategies," Papers 2410.09435, arXiv.org.
    • Handle: RePEc:arx:papers:2410.09435
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    References listed on IDEAS

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    1. M. McManus & Richard E. Quandt, 1961. "Comments on the Stability of the Cournot Oligipoly Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 136-139.
    2. Reinganum, Jennifer F., 1985. "A two-stage model of research and development with endogenous second-mover advantages," International Journal of Industrial Organization, Elsevier, vol. 3(3), pages 275-292, September.
    3. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    4. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
    5. Nikolaos Chrysanthopoulos & George P. Papavassilopoulos, 2021. "Adaptive rules for discrete-time Cournot games of high competition level markets," Operational Research, Springer, vol. 21(4), pages 2879-2906, December.
    6. Gal-Or, Esther, 1985. "First Mover and Second Mover Advantages," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 649-653, October.
    7. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-789, October.
    8. Rassenti, Stephen & Reynolds, Stanley S. & Smith, Vernon L. & Szidarovszky, Ferenc, 2000. "Adaptation and convergence of behavior in repeated experimental Cournot games," Journal of Economic Behavior & Organization, Elsevier, vol. 41(2), pages 117-146, February.
    9. Fiat, Amos & Koutsoupias, Elias & Ligett, Katrina & Mansour, Yishay & Olonetsky, Svetlana, 2019. "Beyond myopic best response (in Cournot competition)," Games and Economic Behavior, Elsevier, vol. 113(C), pages 38-57.
    10. Ding, Zhanwen & Wang, Qiao & Jiang, Shumin, 2014. "Analysis on the dynamics of a Cournot investment game with bounded rationality," Economic Modelling, Elsevier, vol. 39(C), pages 204-212.
    11. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    12. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    13. Franklin M. Fisher, 1961. "The Stability of the Cournot Oligopoly Solution: The Effects of Speeds of Adjustment and Increasing Marginal Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 125-135.
    14. Cánovas, José S. & Puu, Tönu & Ruíz, Manuel, 2008. "The Cournot–Theocharis problem reconsidered," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1025-1039.
    15. Koji Okuguchi, 1970. "Adaptive Expectations in an Oligopoly Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 37(2), pages 233-237.
    16. Cox, James C. & Walker, Mark, 1998. "Learning to play Cournot duopoly strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 36(2), pages 141-161, August.
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