Firms' long-term competitiveness depends on their capability of attaining product and/or process innovations that enable them to appropriate extraordinary rents for a certain period of time. In this paper, we investigate a dynamic interplay between "rms' learning capabilities, market reward structures for the innovation, and other cost factors, establishing an optimal control model for an innovation game context. The analysis helps us to construct a causal relationship map among the key decision elements that identify a dynamic path through which a "rm's learning capability a!ects its competitor's innovation strategy. Numerical examples based on the control model indicate that the "rm with lower learning capability would invest less amount in innovation than would its competitor with higher learning capability. The faster the market reward to the innovation depreciates as the development delays, the more the rate of investment increase slows down as time advances. Likewise, the more the market reward depreciates, the lesser the increase rate of probability that the "rm completes the innovation successfully. The mathematical model in this paper can shed light on the modelling of an innovation game involving dynamic capabilities, and thus contribute to an e!ective innovation decision making.