Patenting in the shadow of independent discoveries by rivals

► This paper studies the decision of whether to apply for a patent. ► Firms innovate stochastically and independently. ► A legal environment characterized by imperfect patent protection and no prior user rights is considered. ► I show how innovators' incentives to patent depend on the nature of innovation and the degree of market competition. ► The optimal level of patent protection is lower with a higher innovation arrival rate or a larger number of firms.