Strategic R&D Investment in Mixed Market Structures: A Differential Game Approach

This thesis provides an exploration of the research by Yanase and Van Long (2023), which analyzes the strategic behavior of large and small firms in research and development (R\&D) investments within mixed market structures. Our study focuses on explaining their differential game framework and the key insights derived from their model. We discuss how firms accumulate cost-reducing knowledge capital over time, emphasizing their use of the Open-Loop Nash Equilibrium (OLNE), its feedback representation, and the Markov Perfect Nash Equilibrium (MPNE) to characterize firm behavior. A central finding of authors’ work is that large firms, due to their existing knowledge capital, lead the process of innovation through continuous R\&D investments, while small firms primarily benefit from knowledge spillovers. Their analysis also highlights a non-linear relationship between competition and innovation, where moderate competition encourages R\&D efforts, but excessive competition reduces profits and weakens incentives to innovate. Additionally, we examine the effects of free entry by small firms, showing that while increased market entry stabilizes output, it intensifies the free-rider problem and discourages R\&D investment by large firms. By systematically explaining the methodology and conclusions of Yanase and Van Long’s model, this thesis aims to make their research more accessible and provide a clearer understanding of the dynamic interactions between firm size, knowledge spillovers, and competition in mixed markets.