# A group has 100 members. Each person can choose to participate or not participate in a common…

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 prisonersâ€™ 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?

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