On the relation between dynamic oligopolistic competition and long-run competitive equilibrimn

Abstract

In this paper we consider a dynamic oligopolistic model where the demand curve is described by a first—order differential equation which relates at each point in time the price of the commodity, the rate of change of the price, and the outputs of all firms in the market. The linear dynamic demand equation is considered as a first—order price adjustment mechanism. Open—loop, feedback and closed—loop Nash equilibria are derived. The corresponding stationary solutions are compared to the static Cournot equilibrium price and the competitive equilibrium price. It is demonstrated that for the “limiting game” (when the constant speed of adjustment reaches infinity) only the stationary open—loop price converges to the static Cournot price. The stationary feedback and a particular closed—loop solution converge to a price which is below the static Cournot price. For the limiting game when the number of firms goes to infinity the Nash equilibrium prices (independent of the information structure assumed) converge to the long—run competitive equilibrium.