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<p>In this paper, we examine an <i>N</i>-firm Cournot oligopoly game, where the market is characterized by a nonlinear demand function and the firms are boundedly rational to adopt the adjustment mechanism of local monopolistic approximation. To discuss the effects of different levels of decreasing returns to scale, the model employs quadratic cost functions. We transform the <i>N</i>-dimensional iteration map that characterizes the model into a one-dimensional aggregate map, allowing us to explore the dynamics of the original model. Accordingly, we derive closed-form solutions for the non-vanishing equilibrium, conduct a comparative static analysis, and investigate the local stability. In addition, using symbolic computation methods, we analytically explore periodic orbits with low orders and analyze their local stability. We derive the existence of 3-cycle orbits in the aggregate map and thus prove that the model may be chaotic in the sense of Li–Yorke.</p>

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Periodic and Chaotic Dynamics of an Oligopoly with Nonlinear Demand and N Firms

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Xiaoliang Li,
  • Bo Li

摘要

In this paper, we examine an N-firm Cournot oligopoly game, where the market is characterized by a nonlinear demand function and the firms are boundedly rational to adopt the adjustment mechanism of local monopolistic approximation. To discuss the effects of different levels of decreasing returns to scale, the model employs quadratic cost functions. We transform the N-dimensional iteration map that characterizes the model into a one-dimensional aggregate map, allowing us to explore the dynamics of the original model. Accordingly, we derive closed-form solutions for the non-vanishing equilibrium, conduct a comparative static analysis, and investigate the local stability. In addition, using symbolic computation methods, we analytically explore periodic orbits with low orders and analyze their local stability. We derive the existence of 3-cycle orbits in the aggregate map and thus prove that the model may be chaotic in the sense of Li–Yorke.