Consider a village of ten people. If a nearby mosquito-infested swamp is drained, then all ten people receive a benefit of b. People simultaneously choose either to volunteer for the project or not. If at least five people volunteer, then the swamp is drained. Otherwise, it is not. Each person who volunteers incurs a cost of c.
a. If b > c, what are the pure-strategy Nash equilibria of this game? Explain your reasoning.
b. If b < c, show that there is a unique Nash equilibrium of this game? Explain your reasoning.
c. In words, why can a change in expectations of other players’ behavior lead to provision of the public good in part a but not part b?