We consider a two-player infinite-horizon discrete-time game where the players invest in R&D in order to develop a new technology to reduce production costs. We compute firms’ equilibrium R&D investment strategy as a function of the level of knowledge in the economy. The latter changes endogenously with firms’ decisions to invest in R&D. We show that firms do not invest in R&D if the knowledge level is too low, while both firms do R&D when the level of knowledge is high. However, there is an intermediate knowledge region where there are two pure Nash equilibria: either no firm does R&D or both firms do R&D. Multiplicity of equilibria leads generally to a challenging selection problem. In our context, it is shown that the case of both firms investing in R&D can be Pareto-dominating for both players. It follows that government actions which allow an economy to increase the level of knowledge above a threshold may be welfare enhancing.