A Differential Game Analysis of Firms’ Clean Technology Innovation with Spillover Effects and Learning-by-Doing in a Duopoly Market

In this paper, we develop a differential game model of firms’ clean technology (cleantech) research and development (R&D) with spillover effects and learning-by-doing in a duopoly market. A significant feature of our study is that each firm’s instantaneous investment cost function in cleantech R&D depends not only on the R&D investment itself but also on the accumulation of knowledge in cleantech R&D. Furthermore, the rate of change in each firm’s accumulation of cleantech R&D knowledge is treated as a state variable. The main objective of this paper is to investigate firms’ cleantech investment behavior and the effects of cleantech spillover and learning-by-doing on cleantech progress, both in cases of R&D competition and R&D cooperation. Additionally, we derive the general solutions of the model and discuss the results using numerical examples. We demonstrate that private and social incentives towards R&D cooperation align across all admissible levels of the clean technological spillover, which characterizes innovative activity, as well as the learning rate and growth rate of knowledge accumulation in cleantech investment, which characterizes learning-by-doing activity.