Symmetric research joint ventures: Cooperative substitutes and complements

We introduce the concept of cooperative substitutes and complements, and use it to throw light on the conditions for a research joint venture to choose equal levels of R&D by all member firms. We show that the second-order conditions for a symmetric optimum take a particularly simple form, ruling out both excessive cooperative substitutability and excessive cooperative complementarity, and nesting conditions already derived in the literature. Finally we explore the implications of our results for the comparison between research joint ventures and a non-cooperative equilibrium.