Exam 27: A: Game Theory

(See Problem 2.) A small community has 40 people, each of whom has a wealth of $16,000. 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 b times the total amount of money contributed by individuals in the community.

(See Problem 7.) If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 120 + 0.20X. What is a long-run equilibrium attendance for this club?

(See Problem 7.) If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 48 + 0.40X. What is a long-run equilibrium attendance for this club?

(See Problem 2.) A small community has 10 people, each of whom has a wealth of $17,000. 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.

(See Problem 7.) If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 56 + 0.60X. What is a long-run equilibrium attendance for this club?

(See Problem 1.) Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $200. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium?

(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 $50,000 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 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 $60,000 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 1.) Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $400. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium?

(See Problem 1.) Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $100. If both play the strategy stay, then each gets a payoff of $800. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium?

(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 $10,000 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 10 people, each of whom has a wealth of $5,000. 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 b times the total amount of money contributed by individuals in the community.

(See Problem 7.) If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 30 + 0.70X. What is a long-run equilibrium attendance for this club?

(See Problem 2.) A small community has 10 people, each of whom has a wealth of $19,000. 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.

(See Problem 1.) Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $300. If both play the strategy stay, then each gets a payoff of $600. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium?

(See Problem 2.) A small community has 20 people, each of whom has a wealth of $12,000. 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 b 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 $80,000 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 1.) Alice and Betsy are playing a game in which each can play either of two strategies, leave or stay. If both play the strategy leave, then each gets a payoff of $100. If both play the strategy stay, then each gets a payoff of $400. If one plays stay and the other plays leave, then the one who plays stay gets a payoff of $C and the one who plays leave gets a payoff of $D. When is the outcome where both play leave a Nash equilibrium?

(See Problem 2.) A small community has 40 people, each of whom has a wealth of $5,000. 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 b times the total amount of money contributed by individuals in the community.

(See Problem 7.) If the number of persons who attend the club meeting this week is X, then the number of people who will attend next week is 80 + 0.20X. What is a long-run equilibrium attendance for this club?