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In this paper, we present a game-theoretic model describing voluntary socialdistancing during the spread of an epidemic. The payoffs of the agents dependon the social distancing they practice and on the probability of gettinginfected. We consider two types of agents, the non-vulnerable agents who have asmall cost if they get infected, and the vulnerable agents who have a highercost. For the modeling of the epidemic outbreak, we consider a variant of theSIR (Susceptible-Infected-Removed) model involving populations of susceptible,infected, and removed persons of vulnerable and non-vulnerable types. The Nashequilibria of this social distancing game are studied. The main contribution ofthis work is the analysis of the case where the players, desiring to achieve alow social inequality, pose a bound on the variance of the payoffs. In thiscase, we introduce and characterize a notion of Generalized Nash Equilibrium(GNE) for games with a continuum of players. Through numerical studies, we showthat inequality constraints result in a slower spread of the epidemic and animproved cost for the vulnerable players. Furthermore, it is possible thatinequality constraints are beneficial for non-vulnerable players as well.

Nash Social Distancing Games with Equity Constraints: How Inequality Aversion Affects the Spread of Epidemics