A group has 100 members. Each person can choose to participate or not participate in a common project. If n of them participate in the project, then each participant derives the benefit p(n) 5 n, and...

A group has 100 members. Each person can choose to participate or not participate in a common project. If n of them participate in the project, then each participant derives the benefit p(n) 5 n, and each of the (100 2n) shirkers derives the benefit s(n) 5 4 1 3n.

(a) Is this an example of a prisoners’ dilemma, a game of chicken, or an assurance game?

(b) Write the expression for the total benefit of the group.

(c) Show, either graphically or mathematically, that the maximum total benefit for the group occurs when n = 74.

(d) What difficulties will arise in trying to get exactly 74 participants and allowing the remaining 26 to shirk?

(e) How might the group try to overcome these difficulties?