A mathematical analysis of public avoidance behavior during epidemics using game theory

Abstract

The decision of individuals to engage in public avoidance during epidemics is modeled and studied using game theory. The analysis reveals that the set of Nash equilibria of the model, as well as how the equilibria compare to the social optimum, depend on the contact function that governs the rate at which encounters occur in public. If the contact ratio - defined to be the ratio of the contact rate to the number of people out in public - is increasing with the number of people out in public, then there exists a unique Nash equilibrium. Moreover, in equilibrium, the amount of public avoidance is too low with respect to social welfare. On the other hand, if the contact ratio is decreasing in the number of people out in public, then there can be multiple Nash equilibria, none of which is in general socially optimal. Furthermore, the amount of public avoidance in equilibrium with a decreasing contact ratio is too high in that social welfare can be increased if more susceptible individuals choose to go out in public. In the special case where the contact ratio does not vary with the number of people out in public, there is a unique Nash equilibrium, and it is also the socially optimal outcome.