Asked by Ramon Gonzalez on Jun 11, 2024
Verified
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.
Public Entertainment
Activities and events intended to amuse or interest the general public, often organized by governmental or community groups.
Dominant Strategy
In game theory, a strategy that is the best for a player to follow regardless of the strategies chosen by other players in the game.
Wealth
The accumulation of valuable financial assets or tangible possessions that can be used or exchanged to procure goods and services.
- Evaluate the role of dominant strategies within the framework of strategic interactions in games.
- Learn about the configuration of public goods dilemmas and their significance for cooperative activities.
- Pinpoint the specific situations that result in cooperation or defection during public goods games.
Verified Answer
NI
Nipuna Ilukpitiye GedaraJun 13, 2024
Final Answer :
B
Explanation :
To determine the best choice, we need to consider the payoffs for each possible outcome.
If everyone contributes, the total amount in the public entertainment fund will be $16,000 (40 x $400). Each individual will then receive a benefit of b x $16,000 / 40 = $400b. However, they will also have to pay $400, resulting in a net benefit of $400b - $400.
If nobody contributes, there will be no public entertainment fund, and each individual will receive no benefit but also not have to pay anything, resulting in a net benefit of 0.
Therefore, the best choice depends on the value of b:
- If 40b > $1, everyone is better off contributing to the public entertainment fund, as their net benefit will be positive ($400b - $400 > 0).
- If 40b < $1, everyone is better off not contributing, as their net benefit will be higher without paying anything (0 > $400b - $400).
In other words, if the value of b is high enough, the benefits of contributing to the public entertainment fund outweigh the costs, and contributing becomes the dominant strategy for everyone. However, if the value of b is too low, nobody has an incentive to contribute, and not contributing becomes the dominant strategy.
Therefore, the correct choice is B.
If everyone contributes, the total amount in the public entertainment fund will be $16,000 (40 x $400). Each individual will then receive a benefit of b x $16,000 / 40 = $400b. However, they will also have to pay $400, resulting in a net benefit of $400b - $400.
If nobody contributes, there will be no public entertainment fund, and each individual will receive no benefit but also not have to pay anything, resulting in a net benefit of 0.
Therefore, the best choice depends on the value of b:
- If 40b > $1, everyone is better off contributing to the public entertainment fund, as their net benefit will be positive ($400b - $400 > 0).
- If 40b < $1, everyone is better off not contributing, as their net benefit will be higher without paying anything (0 > $400b - $400).
In other words, if the value of b is high enough, the benefits of contributing to the public entertainment fund outweigh the costs, and contributing becomes the dominant strategy for everyone. However, if the value of b is too low, nobody has an incentive to contribute, and not contributing becomes the dominant strategy.
Therefore, the correct choice is B.
Learning Objectives
- Evaluate the role of dominant strategies within the framework of strategic interactions in games.
- Learn about the configuration of public goods dilemmas and their significance for cooperative activities.
- Pinpoint the specific situations that result in cooperation or defection during public goods games.