  During a pandemic people have to find a trade-off between meeting others and
staying safely at home. While meeting others is pleasant, it also increases the
risk of infection. We consider this dilemma by introducing a game-theoretic
network creation model in which selfish agents can form bilateral connections.
They benefit from network neighbors, but at the same time, they want to
maximize their distance to all other agents. This models the inherent conflict
that social distancing rules impose on the behavior of selfish agents in a
social network. Besides addressing this familiar issue, our model can be seen
as the inverse to the well-studied Network Creation Game by Fabrikant et al.
[PODC 2003] where agents aim at being as central as possible in the created
network. Thus, our work is in-line with studies that compare minimization
problems with their maximization versions.
  We look at two variants of network creation governed by social distancing. In
the first variant, there are no restrictions on the connections being formed.
We characterize optimal and equilibrium networks, and we derive asymptotically
tight bounds on the Price of Anarchy and Price of Stability. The second variant
is the model's generalization that allows restrictions on the connections that
can be formed. As our main result, we prove that Swap-Maximal Routing-Cost
Spanning Trees, an efficiently computable weaker variant of Maximum
Routing-Cost Spanning Trees, actually resemble equilibria for a significant
range of the parameter space. Moreover, we give almost tight bounds on the
Price of Anarchy and Price of Stability. These results imply that, compared the
well-studied inverse models, under social distancing the agents' selfish
behavior has a significantly stronger impact on the quality of the equilibria,
i.e., allowing socially much worse stable states.
