  A key challenge in responding to public health crises such as COVID-19 is the
difficulty of predicting the results of feedback interconnections between the
disease and society. As a step towards understanding these interconnections, we
pose a simple game-theoretic model of a global pandemic in which individuals
can choose where to live, and we investigate the global behavior that may
emerge as a result of individuals reacting locally to the competing costs of
isolation and infection. We study the game-theoretic equilibria that emerge
from this setup when the population is composed of either selfish or altruistic
individuals. First, we demonstrate that as is typical in these types of games,
selfish equilibria are in general not optimal, but that all stable selfish
equilibria are within a constant factor of optimal. Second, there exist
infinitely-many stable altruistic equilibria; all but finitely-many of these
are worse than the worst selfish equilibrium, and the social cost of altruistic
equilibria is unbounded. Our work is in sharp contrast to recent work in
network congestion games in which all altruistic equilibria are socially
optimal. This suggests that a population without central coordination may react
very poorly to a pandemic, and that individual altruism could even exacerbate
the problem.
