The vaccine immunizes but can cause complications, even death. The vaccine worsens the patient’s condition if the patient is both infected and vaccinated at the same time. The vaccine stops the flu from spreading, if enough people are vaccinated. If enough people are vaccinated, the patient should not be vaccinated since the infection stopped spreading.

Thus, if everyone is just like everyone else, there is no pure strategy equilibrium, and the patient should throw a coin to choose whether to take the injection. On the other hand, if some are more equal than others, they can skip on the vaccine and let others suffer for their good.

Only computer scientists understand why a pure strategy exists if computer scientists behave differently from normal people. So, the pure strategy is to vaccinate everyone except for computer scientists.

Flawless, isn’t it?