We study a model of innovation with a large number of firms that create new technologiesby combining several discrete ideas. These ideas can be acquired by private investment orvia social learning. Firms face a choice between secrecy, which protects existing intellectualproperty, and openness, which facilitates learning from others. Their decisions determine
interaction rates between firms, and these interaction rates enter our model as link proba-bilities in a learning network. Higher interaction rates impose both positive and negative
externalities on other firms, as there is more learning but also more competition. We showthat the equilibrium learning network is at a critical threshold between sparse and dense
networks. At equilibrium, the positive externality from interaction dominates: the innova-tion rate and even average firm profits 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 fromcriticality. One policy solution is to introduce informational intermediaries, such as publicinnovators who do not have incentives to be secretive. These intermediaries can facilitate ahigh-innovation equilibrium by transmitting ideas from one private firm to another.