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, 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 20.

Question

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.

Quizplus · Accepted Answer

Option A correctly summarizes the outcomes based on the value of b. If b is greater than 1/20, it is better for everyone to contribute, and if b is less than 1/20, it is better for everyone to not contribute. This is because if everyone contributes, the benefit for each person is b times the total contribution, which is 20 times the individual contribution. But if b is less than 1/20, the benefit for each person is less than the individual contribution, so it is better to not contribute. Option B incorrectly suggests that there is a dominant strategy equilibrium in which everyone contributes, which is only true if b is greater than 1/20. Option C incorrectly suggests that everyone is worse off if all contribute, which is only true if b is greater than 1/20. Option D is incorrect because it ignores the possibility of a dominant strategy equilibrium in which everyone contributes if b is greater than 1/20. Option E is also incorrect because it suggests that everyone can have a dominant strategy to contribute if b is simply greater than 20, which is not true - it must be greater than 1/20.

A Small Community Has 20 People, Each of Whom Has