Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 11 2 2026 09 04 Simultaneous Profit Optimization and Market Price Agreement in Networks of LTI Duopoly Systems 352 362 2141 10.22128/ansne.2026.3344.1221 EN Mehrasa Ayatollahi Department of Mathematics, Payame Noor University, Tehran, Iran 0000-0003-0542-7137 Journal Article 2026 06 01 This paper studies networks of dynamic duopoly systems with the objectives of maximization of firms' discounted profits and of convergence of market prices in all markets. We model each duopoly as a dynamical process of price adjustment, driven by production decisions of firms. The profit maximization problem is reformulated as a quadratic optimal control problem by representing the dynamics of the duopoly in a linear time-invariant (LTI) state-space form. In order to impose the price convergence between the markets, a consensus term is added to the cost function. We use the Hamilton--Jacobi--Bellman (HJB) approach to derive a control law that encourages profit maximization and market price convergence over a finite time horizon. The proposed framework reformulates the dynamic duopoly problem in networked markets within an optimal control framework, allowing simultaneous profit optimization and market price coordination. https://ansne.du.ac.ir/article_2141_1c1a9ca486183d2e93d538ee2cc3eff2.pdf