  The spontaneous behavioral changes of the agents during an epidemic can have
significant effects on the delay and the prevalence of its spread. In this
work, we study a social distancing game among the agents of a population, who
determine their social interactions during the spread of an epidemic. The
interconnections between the agents are modeled by a network and local
interactions are considered. The payoffs of the agents depend on their benefits
from their social interactions, as well as on the costs to their health due to
their possible contamination. The information available to the agents during
the decision making plays a crucial role in our model. We examine two extreme
cases. In the first case, the agents know exactly the health states of their
neighbors and in the second they have statistical information for the global
prevalence of the epidemic. The Nash equilibria of the games are studied and,
interestingly, in the second case the equilibrium strategies for an agent are
either full isolation or no social distancing at all. Experimental studies are
presented through simulations, where we observe that in the first case of
perfect local information the agents can affect significantly the prevalence of
the epidemic with low cost for their sociability, while in the second case they
have to pay the burden of not being well informed. Moreover, the effects of the
information quality (fake news), the health care system capacity and the
network structure are discussed and relevant simulations are provided, which
indicate that these parameters affect the size, the peak and the start of the
outbreak, as well as the possibility of a second outbreak.
