  The COVID-19 lockdowns have created a significant socioeconomic impact on our
society. In this paper, we propose a population vaccination game framework,
called EPROACH, to design policies for reopenings that guarantee post-opening
public health safety. In our framework, a population of players decides whether
to vaccinate or not based on the public and private information they receive.
The reopening is captured by the switching of the game state. The insights
obtained from our framework include the appropriate vaccination coverage
threshold for safe-reopening and information-based methods to incentivize
individual vaccination decisions. In particular, our framework bridges the
modeling of the strategic behaviors of the populations and the spreading of
infectious diseases. This integration enables finding the threshold which
guarantees a disease-free epidemic steady state under the population's Nash
equilibrium vaccination decisions. The equilibrium vaccination decisions depend
on the information received by the agents. It makes the steady-state epidemic
severity controllable through information. We find out that the externalities
created by reopening lead to the coordination of the rational players in the
population and result in a unique Nash equilibrium. We use numerical
experiments to corroborate the results and illustrate the design of public
information for responsible reopening.
