The Vaccination Game

If people face the possibility of catching an infectious disease and have the option of a completely effective vaccine against it, how many will choose to be vaccinated? Clearly not all, as if everyone else is vaccinated there is no incentive for me to join them: I face no risk. Likewise if no one is vaccinated then everyone has a strong incentive to be vaccinated, so we do not expect that no one being vaccinated is an equilibrium. It seems from this that there should be an interior solution with some but not all of the population being vaccinated. But who, and how many, will be vaccinated? We answer this question. We also show that if the vaccine is not completely e¤ective the game may change radically, switching from strategic subsitutability to complementarity and resembling that of a Class 1 IDS problem such as airline security, with potential for tipping and cascading. We also give a sufficient condition for voluntary vaccintion to eradicate a disease and derive the demand curve for vaccintion as a function of cost and disease prevelance. We can also calculate the subsidy needed to align the Nash equilibrium with the socially optimal outcome and the subsidy needed to ensure disease eradication.