Mixed Equilibrium Vaccination Patterns in a Contagion Network

If individuals contract diseases from anticipated interactions and can vaccinate to protect themselves, a pure-strategy Nash equilibrium vaccination pattern arises in the contagion network. But when individuals cannot coordinate to achieve a pure equilibrium, they may choose a mixture of vaccination strategies. This paper compares the vaccination game to the game of chicken to demonstrate the rationale for the mixed-strategy equilibrium and discovers its unique features. Firstly, while the social optimum requires vaccinating a few high-externality agents, extreme deviations where everyone or no one vaccinated become possible. Furthermore, the central player in a star network should get the vaccine first but is less likely to vaccinate than others in the mixed equilibrium. Lastly, the mixed equilibrium generates the same social loss as the untargeted mandate, which is always worse than the suboptimal pure equilibrium.