Simultaneous Profit Optimization and Market Price Agreement in Networks of LTI Duopoly Systems

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.

کلیدواژه ها:

Duopoly System ، Price Agreement ، LTI Control System ، Optimal control ، State Consensus