Dynamic Duopoly Game: Differential Game Theoretic Approach

Abstract

Output variation type Cournot duopoly game is studied within the framework of differential game theory. Necessary conditions for a general case are developed in their typical coupled form and the difference between an open-loop control (supply adjustment) and a closed-loop control is pointed out. Linear dynamic market demand function and quadratic cost functions case is then studied in detail and analytic expressions for the optimal Cournot controls are obtained in terms of the solution of a set of differential equations for a finite horizon case (t ε [0, T)) and, a set of algebraic equations for an infinite horizon case (t ε [0, ∞]).