A research institute in Israel claims to be close to developing a vaccine for the corona virus. They claim that this vaccine may be available as early as May 2020. Others have expressed fears that while the vaccine will stop infection by the virus but may have serious side effects. In a small town in Oregon the two residents, Joe-Bob and Bobby-Joe are trying to decide whether to get inoculated with vaccine once it becomes available. They live in a remote location and if not inoculated are mostly likely to contract the virus from each other. The two residents must simultaneously choose to be inoculated or not.

(a) a payoff matrix for this game such that in equilibrium neither resident chooses to take the vaccine.

(b) a payoff matrix such that only one of the residents chooses to take the vaccine, but where we cannot say which one it will be.

(c) Using the payoffs you provided in part (b) now assume that Joe-Bob gets to choose whether to take the vaccine before Bobby-Joe. Using a game tree explain who takes the vaccine, if anyone does.