Abstract: R&D investment is important for achieving innovative development and industrial upgrading. Based on the perspective of industry R&D competition, this paper explores the internal mechanism of dynamic evolution of the optimal interval for firms' R&D investment by constructing a dynamic optimization model including R&D barrier point and R&D saturation point, and using the time-varying threshold model for empirical tests. We find that firms have an optimal interval of R&D investment that depends on the R&D level of their peers. As the R&D level of the industry increases, the lower bound (R&D barrier point) of the optimal interval rises significantly, while the upper bound (R&D saturation point) decreases significantly. The mechanism analysis reveals that the dynamic evolution of firms' optimal R&D investment interval is influenced considerably by the "Red Queen effect." The risk consequence analysis further shows that achieving the optimal R&D interval enhances a firm's risk-bearing capacity and reduces the likelihood of financial distress. This paper expands the theoretical connotation of industry innovation ecology shaping enterprises' R&D decision-making, and has important implications for leading enterprises to implement an innovation-driven development strategy.

Key words: optimal interval for firms'R&D investment, dynamic evolution, industry R&D competition, time-varying threshold, firm performance