R&D Investments Under Endogenous Cluster Formation

Abstract

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.

Keywords: R&D, cluster formation, oligopoly

JEL Classification: C71, C72, L13, O30