Before revision:  In the second part of the paper we study the equilibrium of the social distancing game and we show that voluntary social distancing will always be socially sub-optimal .
After revision:  In the second part of the paper we study the equilibrium of the social distancing game , in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal .