Open Innovation in a dynamic Cournot duopoly

•An OI process where knowledge spillovers are endogenously determined is analyzed.•A firm may trade off R&D investment against information absorption from the rival.•Higher private R&D investment corresponds to smaller OI absorption effort.•Profits increase as OI absorption increases even at a lower production level.

In recent years Open Innovation (OI) processes have been receiving growing attention from the empirical and theoretical economic literature, where a debate is taking place on the aspects of complementarity or substitutability between internal R&D and OI spillover. By means of a differential game approach, we analyze the case of substitutability in an OI setup in a Cournot duopoly where knowledge spillovers are endogenously determined via the R&D process. The game produces multiple steady states, allowing for an asymmetric solution where a firm may trade off the R&D investment against information absorption from the rival. The technical analysis and the numerical simulations point out that the firm which commits to a higher level of OI absorption produces a smaller output and enjoys higher profits than its rival.