Nash Social Distancing Games with Equity Constraints: How Inequality Aversion Affects the Spread of Epidemics
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In this paper, we present a game-theoretic model describing the voluntary social distancing during the spread of an epidemic. The payoffs of the agents depend on the social distancing they practice and on the probability of getting infected. We consider two types of agents, the vulnerable agents who have a small cost if they get infected, and the non-vulnerable agents who have a higher cost. For the modeling of the epidemic outbreak, a variant of the SIR model is considered, involving populations of susceptible, infected, and recovered persons of vulnerable and non-vulnerable types. The Nash equilibria of this social distancing game are studied. We then analyze the case where the players, desiring to achieve a low social inequality, pose a bound on the variance of the payoffs. In this case, we introduce a notion of Generalized Nash Equilibrium (GNE) for games with a continuum of players and characterize the GNE. We then present some numerical results. It turns out that inequality constraints result in a slower spread of the epidemic and an improved cost for the vulnerable players. Furthermore, it is possible that inequality constraints are beneficial for non-vulnerable players as well.
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