Interaction in prevention: a general theory and an application to COVID-19 pandemic

We study a model introducing interactions in agents' prevention effort, including both the case where agents' efforts reinforce each others and the case where they are conflicting. We characterize best response functions, distinguishing the case of strategic complementarity and the case of strategic substitutability, and determine the features of Nash equilibria in both cases. We find conditions for under- and over-provision of prevention compared to its socially optimal level. Finally, we specialize our model to describe the risk of COVID-19 infection. We show the features of contagion are consistent with the existence of asymmetric equilibria and we provide arguments in favor of policy interventions, such as making face masks mandatory, despite the possibility that they reduce some agents' effort.