Deck 29: Extension: A: Game Theory

Question 1

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.

A)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.
B)If 10b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 10b <1, everybody is better off if nobody contributes than if all contribute.
C)If 10b > 1, there is a dominant strategy equilibrium in which everybody contributes.
D)Everybody is worse off if all contribute than if nobody contributes if b> 1, but if b < 1, everybody is better off if nobody contributes.
E)In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 10.

Answer 1

If 10b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 10b <1, everybody is better off if nobody contributes than if all contribute.

Question 2

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?

A)When D > C and C > $200.
B)Never, since $800 > $200.
C)Whenever D < $800.
D)When $200 > C and D > $800 but not when $800 > D.
E)Whenever $200 > C.

Answer 2

Whenever $200 > C.

Question 3

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.

A)This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $60,000.
B)In the only Nash equilibrium for this game, one partner earns $90,000 and the other earns $40,000.
C)In the only Nash equilibrium for this game, both partners earn $100,000.
D)In the only Nash equilibrium for this game, both partners earn $60,000.
E)This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.

Answer 3

This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $60,000.

Question 4

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?

A)When D > C and C > $100.
B)Never, since $800 > $100.
C)When $100 > C and D > $800 but not when $800 > D
D)Whenever D < $800.
E)Whenever $100 > C.

Question 5

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.

A)This game has a dominant strategy equilibrium in which all 10 citizens contribute $300 to support public entertainment.
B)This game has two Nash equilibria, one in which everybody contributes $300 and one in which no-body contributes $300.
C)This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies.
D)This game has a Nash equilibrium in which 5 people contribute $300 and for public entertainment and 5 people contribute nothing.
E)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.

Question 6

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.

A)In the only Nash equilibrium for this game, both partners earn $100,000.
B)In the only Nash equilibrium for this game, one partner earns $120,000 and the other earns $40,000.
C)In the only Nash equilibrium for this game, both partners earn $90,000.
D)This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $90,000.
E)This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.

Question 7

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.

A)If 40b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 40b < 1, everybody is better off if nobody contributes than if all contribute.
B)Everybody is worse off if all contribute than if nobody contributes if b > 1, but if b < 1, everybody is better off if nobody contributes.
C)If 40b > 1, there is a dominant strategy equilibrium in which everybody contributes.
D)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.
E)In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 40.

Question 8

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?

A)Never, since $800 > $400.
B)When $400 > C and D > $800 but not when $800 > D
C)When D > C and C > $400.
D)Whenever D < $800.
E)Whenever $400 > C

Question 9

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.

A)In the only Nash equilibrium for this game, one partner earns $60,000 and the other earns $40,000.
B)In the only Nash equilibrium for this game, both partners earn $30,000.
C)This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $30,000.
D)In the only Nash equilibrium for this game, both partners earn $100,000.
E)This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.

Question 10

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.

A)This game has a dominant strategy equilibrium in which all 10 citizens contribute $200 to support public entertainment.
B)This game has two Nash equilibria, one in which everybody contributes $200 and one in which nobody contributes $200.
C)This game has a Nash equilibrium in which 5 people contribute $200 and for public entertainment and 5 people contribute nothing.
D)This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies.
E)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.

Question 11

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?

A)When $300 > C and D > $600 but not when $600 > D
B)Never, since $600 > $300.
C)Whenever D < $600.
D)When D > C and C > $300.
E)Whenever $300 > C

Question 12

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.

A)If 40b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 40b < 1, everybody is better off if nobody contributes than if all contribute.
B)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.
C)If 40b > 1, there is a dominant strategy equilibrium in which everybody contributes.
D)Everybody is worse off if all contribute than if nobody contributes if b > 1, but if b < 1, everybody is better off if nobody contributes.
E)In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 40.

Question 13

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.

A)This game has a Nash equilibrium in which 5 people contribute $200 and for public entertainment and 5 people contribute nothing.
B)This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies.
C)This game has two Nash equilibria, one in which everybody contributes $200 and one in which no-body contributes $200.
D)This game has a dominant strategy equilibrium in which all 10 citizens contribute $200 to support public entertainment.
E)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.

Question 14

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?

A)Never, since $400 > $100.
B)Whenever D < $400.
C)When D > C and C > $100.
D)When $100 > C and D > $400 but not when $400 > D.
E)Whenever $100 > C.

Question 15

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.

A)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.
B)If 40b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 40b < 1, everybody is better off if nobody contributes than if all contribute.
C)If 40b > 1, there is a dominant strategy equilibrium in which everybody contributes.
D)Everybody is worse off if all contribute than if nobody contributes if b > 1, but if b < 1, everybody is better off if nobody contributes.
E)In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 40.

Question 16

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.

A)This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $20,000.
B)In the only Nash equilibrium for this game, both partners earn $20,000.
C)In the only Nash equilibrium for this game, one partner earns $50,000 and the other earns $40,000.
D)In the only Nash equilibrium for this game, both partners earn $100,000.
E)This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.

Question 17

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.

A)In the only Nash equilibrium for this game, both partners earn $70,000.
B)In the only Nash equilibrium for this game, one partner earns $100,000 and the other earns $40,000.
C)In the only Nash equilibrium for this game, both partners earn $100,000.
D)This game has two Nash equilibria, one in which each partner has an income of $100,000 and one in which each partner has an income of $70,000.
E)This game has no pure strategy Nash equilibria, but has a mixed strategy equilibrium.

Question 18

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.

A)This game has two Nash equilibria, one in which everybody contributes $200 and one in which nobody contributes $200.
B)This game has a dominant strategy equilibrium in which all 10 citizens contribute $200 to support public entertainment.
C)This game has a Nash equilibrium in which 5 people contribute $200 and for public entertainment and 5 people contribute nothing.
D)This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies.
E)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.

Question 19

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.

A)This game has a dominant strategy equilibrium in which all 10 citizens contribute $100 to support public entertainment.
B)This game has two Nash equilibria, one in which everybody contributes $100 and one in which nobody contributes $100.
C)This game has no Nash equilibrium in pure strategies, but has a Nash equilibrium in mixed strategies.
D)This game has a Nash equilibrium in which 5 people contribute $100 and for public entertainment and 5 people contribute nothing.
E)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.

Question 20

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.

A)If 20b > 1, everybody is better off if all contribute to the public entertainment fund than if nobody contributes, but if 20b < 1, everybody is better off if nobody contributes than if all contribute.
B)If 20b > 1, there is a dominant strategy equilibrium in which everybody contributes.
C)Everybody is worse off if all contribute than if nobody contributes if b > 1, but if b < 1, everybody is better off if nobody contributes.
D)This game has a dominant strategy equilibrium in which nobody contributes anything for public entertainment.
E)In order for there to be a dominant strategy equilibrium in which all contribute, it must be that b > 20.

Question 21

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?

A)120
B)600
C)240
D)150
E)30

Question 22

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?

A)42.86
B)60
C)100
D)30
E)70

Question 23

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?

A)400
B)80
C)100
D)160
E)20

Question 24

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?

A)96
B)80
C)120
D)48
E)32

Question 25

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?

A)93.33
B)112
C)140
D)56
E)84