Interaction in Prevention: A General Theory and an Application to COVID-19 Pandemic

Prevention efforts often involve spillovers, positive or negative, on other individuals, but this is neglected by standard models of risk prevention. We analyze strategic interaction between decision makers whose effort affects each other's risk. We characterize response functions and Nash equilibria, providing proof of existence and analyzing the Pareto efficiency and possible multiplicity of equilibria. We then analyze the optimal effort level from a social point of view, finding conditions under which Nash equilibria are characterized by under- or over-provision of effort, which calls for policy interventions. Finally, we specialize our model to describe the risk of COVID-19 infection. The features of contagion are consistent with the existence of asymmetric equilibria where the high effort exerted by one decision maker pushes another to exert low effort. Moreover, socially optimal mandatory policies, for instance concerning face masks, can cause a decision maker to decrease exerted effort.