R&D Investments under Endogenous Cluster Formation

We study investments in R&D and the formation of R&D clusters of firms which are competitors in the market. In a three stage game, firms first decide on the budget allocated to their R&D department, then form research clusters and finally compete in quantities. The second stage cluster formation is modeled by the unanimity game introduced in Bloch(1995). We show that for any distribution of R&D investments, an equilibrium of the second stage cluster formation exists and is generically unique up to a permutation of firms which chose the same investment. Restricting to two investment levels in the first stage, we provide a complete characterization of the equilibria of the three stage game. We show that for some range of investment costs, equilibria with no-investment co-exist with equilibria where a large fraction or even all firms invest in R&D. Furthermore, in the high-investment equilibrium firms over–invest compared to a scenario where research clusters are ex-ante fixed and also compared to the welfare optimum. JEL Classifications: C71, C72, L13, O30