A group has 100 members. Each person can choose to participate or not participate in a common project. Ifnof them participate in the project, theneach participant derives the benefitp(n)=n, and each of the (100n) shirkers derives the benefits(n)=3n180 .

1. Is this collective-action problem an example of a prisoners' dilemma, a game of chicken, or an assurance game?
2. Write the expression for the total social payoff of the group.
3. Show, either graphically or mathematically, that the maximum total social payoff for the group occurs whenn=100.