Differential games of R&D competition with switching dynamics

This paper investigates a differential game model of R&D competition, starting with a two-stage structure and then extending this structure to a generalized multi-stage model.The two-stage model captures distinct efficiency dynamics, and the Nash equilibrium analysis reveals optimal strategies for resource allocation. The multi-stage extension generalizes these insights, providing a broader view of firms' strategic adjustments. The study identifies these key properties: the consistent ratio of control efforts across different stages, the structural uniformity of Nash equilibrium strategies, and the continuity of these properties in multi-stage scenarios. These findings enhance the understanding of strategic behavior in competitive innovation environments.