This paper considers a non‐cooperative R&D network formation game. Instead of concentrating on R&D cooperation among firms, the paper focuses on one‐way externality flow in which each firm forms links in the attempt to acquire others' R&D knowledge. It is assumed that a firm has an internal R&D strategy (in‐house R&D) and an external R&D strategy (knowledge acquisition) and that these two strategic options are substitutes. It is found that a firm will trade off its own investment cost and acquisition cost. Consequently, the equilibrium network is empty when investment or linkage cost is high, whereas the equilibrium network is of core–periphery structure when both costs are relatively low, with core firms investing in R&D activities and periphery firms accessing R&D knowledge from core ones. The paper also investigates efficiency and the conclusion is that although an efficient R&D network is a periphery‐sponsored star, the core firm tends to underinvest in Nash equilibrium.