A Dynamic Model of Competitive Entry Response

I develop a dynamic investment game with a "memoryless" R&D process in which an incumbent and an entrant can invest in a new technology, and the entrant can also invest in the old technology. I show that an increase in the probability of successfully implementing a technology can cause the incumbent to reduce its investment. Under certain conditions, if the success probability is high, the incumbent allows the entrant to win the new technology so that firms reach an equilibrium in which they use different technologies, and threats of retaliation prevent attacks; but if the success probability is low, such an equilibrium cannot be sustained, and both firms eventually implement both technologies