Optimal dynamics of technology and price in a duopoly market

Abstract

This article examines a case where the demand of a new product follows an applied diffusion model influenced by innovation and price differential effects, and the potential market size expands as the technology level embodied in the product advances. For a duopoly, we set up a differential game model and derived open-loop Nash equilibrium solutions, showing that the optimal dynamics between the competitors' technology and price levels depend on the relative magnitude of innovation and price differential coefficients. If the price differential coefficients of the two competitors are symmetrical, the optimal prices become constant and in general the technology levels increase.