Causation and the incentives of multiple injurers

•But-for causation does not necessarily entail efficient incentives.•It may fail to do so when the harm function is submodular.•We compare but-for causation with the NESS-test and the Shapley value.•We find reasons to favor the Shapley-value. Under the but-for requirement of causation, a tort injurer cannot be held liable for more than the difference between the loss the victim would have suffered if the injurer had not been negligent, and the loss that is in reality suffered. We ask whether this causation requirement yields efficient precaution in the context of two or more injurers. Contrary to a widely accepted view, we find that but-for causation may lead to the existence of an inefficient Nash-equilibrium. We characterize when this may occur and compare those instances with precedent in which courts have not required but-for causation. Moreover, we ask whether alternative concepts of causation do better than but-for causation in terms of incentives. We find that while both the NESS-test and the Shapley provide optimal incentives when injurers act simultaneously, there are reasons for considering the Shapley-value as the more satisfactory concept of causation.