Self-Protection, Strategic Interactions, and the Relative Endogeneity of Disease Risks

Self-protection is a key behavior that influences infectious disease risks. Spillovers in disease protection create different types of strategic interactions. Under certain conditions, multiple Nash equilibria may arise with the possibility of coordination failure involving excessively low self-protection, in which case individuals' expectations of others' efforts determine which outcome arises. In prior studies, assumed technical relations between self-protection and infection probabilities drove the strategic interactions. We demonstrate that strategic relations can be endogenously determined and depend on the relative endogeneity of risk (RER), defined here as the degree to which individuals can take control of their own risks in a strategic setting. The potential for coordination failure may arise when RER is sufficiently small, whereas larger levels of RER may eliminate this possibility to ensure larger levels of self-protection. We find that imposing a behaviorally-dependent indemnity may increase RER to eliminate the possibility of coordination failure. We apply our analysis to the problem of livestock disease and illustrate the theory using a numerical example of the 2001 United Kingdom foot-and-mouth disease epidemic.