This paper introduces a framework to study innovation in a strategic setting, in which innovators allocate their resources between exploration and exploitation in continuous time. Exploration creates public knowledge, while exploitation delivers private benefits. Through the analysis of a class of Markov equilibria, we demonstrate that knowledge spillovers accelerate knowledge creation and expedite its availability, thereby encouraging innovators to increase exploration. The prospect of the ensuing superior long-term innovations further motivates exploration, giving rise to a positive feedback loop. This novel feedback loop can substantially mitigate the free-riding problem arising from knowledge spillovers.