  We study a model of innovation with a large number of firms that create new
technologies by combining several discrete ideas. These ideas are created via
private investment and spread between firms. Firms face a choice between
secrecy, which protects existing intellectual property, and openness, which
facilitates learning from others. Their decisions determine interaction rates
between firms, and these interaction rates enter our model as link
probabilities in a learning network. Higher interaction rates impose both
positive and negative externalities, as there is more learning but also more
competition. We show that the equilibrium learning network is at a critical
threshold between sparse and dense networks. At equilibrium, the positive
externality from interaction dominates: the innovation rate and welfare would
be dramatically higher if the network were denser. So there are large returns
to increasing interaction rates above the critical threshold. Nevertheless,
several natural types of interventions fail to move the equilibrium away from
criticality. One effective policy solution is to introduce informational
intermediaries, such as public innovators who do not have incentives to be
secretive. These intermediaries can facilitate a high-innovation equilibrium by
transmitting ideas from one private firm to another.
