Shutdown and compliance decisions in the face of a viral pandemic: A game between governments and citizens

During viral pandemics, governments throughout the world face many complicated and important decisions, such as whether and how to implement a shutdown. In response to shutdown measures that are enacted by governments, citizens are then forced to make decisions regarding whether to comply (and stay home) or violate (and leave their residence for non-essential reasons). To the best of our knowledge, these shutdown and compliance interactions between governments and citizens have received limited attention from the scientific community. To address this gap, we start by developing a single-leader multiple-follower game-theoretic model to study the optimal decisions of the government, who wants to minimize her total cost of implementing a shutdown while balancing societal infection risks, and the public, which wants to minimize their total cost of compliance and individual infection risks. In this initial version of the game, the government selects whether or not to implement a shutdown, while the public decides whether to comply with the government's safety guidelines. We then extend this version of the game by modeling a continuous-choice government, where she can implement a total shutdown, no safety measures at all, or anything between those extremes. We solve both models analytically, resulting in closed-form equilibrium solutions. Using data related to COVID-19, we conduct sensitivity analyses to study how the equilibrium strategies change as the values of the model parameters fluctuate. Our models and analyses offer important and relevant insights into optimal decision making in this setting, and also apply in situations in which infections spread at a rapid rate but may not cause severe illness, such as the case of the Omicron variant of COVID-19. In these scenarios, the models recommend that the government does not implement a shutdown, and instead encourages the public to follow safety measures to avoid infections.