Exam 27: A: Game Theory

(See Problem 2.) A small community has 10 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $300 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is .50 times the total amount of money contributed by individuals in the community.

(See Problem 2.) A small community has 10 people, each of whom has a wealth of $2,000. Each individual must choose whether to contribute $100 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is .65 times the total amount of money contributed by individuals in the community.

(See Problem 4, the Stag Hunt.) Two partners start a business. Each has two possible strategies, spend full time or secretly take a second job and spend only part time on the business. Any profits that the business makes will be split equally between the two partners, regardless of whether they work full time or part time for the business. If a partner takes a second job, he will earn $20,000 from this job plus his share of profits from the business. If he spends full time on the business, his only source of income is his share of profits from this business. If both partners spend full time on the business, total profits will be $200,000. If one partner spends full time on the business and the other takes a second job, the business profits will be $80,000. If both partners take second job, the total business profits are $20,000.

(See Problem 2.) A small community has 40 people, each of whom has a wealth of $3,000. Each individual must choose whether to contribute $400 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is b times the total amount of money contributed by individuals in the community.

(See Problem 2.) A small community has 10 people, each of whom has a wealth of $18,000. Each individual must choose whether to contribute $200 or $0 to the support of public entertainment for their community. The money value of the benefit that a person gets from this public entertainment is .80 times the total amount of money contributed by individuals in the community.