I am struggling to solve this question and is hoping that I can get some help:
Suppose that $B>2$ individuals want to start a cafe. At least $A$ people need to maintain the cafe where $1<A<B$. Each person receives a payoff of $C$ from the cafe regardless if they maintain the cafe or not. Maintaining the cafe incurs a cost of $D$.
Suppose that $C<D$, what are the pure strategy Nash equilibria? What are the pure strategy Nash equilibria if $C>D$?
If $C<D$, nobody wants to maintain the cafe, so the only Nash equilibrium is that nobody does os.
If $C>D$, having the cafe open without incurring costs is the first best, and having the cafe open and maintaining it is the second best. So the Nash equilibria in pure strategies are all those strategic profiles where $A$ people pay and $B-A$ do not pay.