Nonlinear Dynamics and Stability in a Cournot Duopoly Model with Cobb–Douglas Technology and Quadratic Costs

Description

In this paper, we propose a modified version of the classical Cournot competition framework in which each firm operates under a quadratic cost function that includes a fixed-cost component. The model extends the traditional setting by incorporating a Cobb–Douglas production structure, allowing firms to differ in productivity levels and factor shares. This non-symmetric technological configuration captures heterogeneity in production efficiency and cost composition, thereby reflecting more realistic competitive market conditions. We derive the best-response functions of both firms and obtain the corresponding Nash Equilibrium quantities explicitly in terms of the production and cost parameters. The resulting system generates nonlinear dynamics for the evolution of outputs. We analyze the fixed points of this dynamic system and investigate how technological and cost heterogeneity influence their location and multiplicity. A complete local stability analysis of all equilibria is conducted. We classify the types of convergence and identify parameter regimes leading to qualitative changes in system behavior. In particular, we determine the bifurcation values at which stability is lost and dynamic patterns shift, highlighting the critical role of technological asymmetry in shaping market dynamics.