Scenario 13.7
Consider the game below about funding and construction of a dam to protect a 1,000-person town. Contributions to the Dam Fund, once made, cannot be recovered, and all citizens must contribute $1,000 to the dam in order for it to be built. The dam, if built, is worth $70,000 to each citizen.
-In the game in Scenario 13.7, the strategy pair that pays:
A) $69,000 to each player is the only equilibrium.
B) ($0, -$1000) is the only equilibrium.
C) (-$1000, $0) is the only equilibrium.
D) $0 to each player is the only equilibrium.
E) $69,000 to each player and the strategy pair that pays $0 to each player are equilibria.

Question

Scenario 13.7
Consider the game below about funding and construction of a dam to protect a 1,000-person town. Contributions to the Dam Fund, once made, cannot be recovered, and all citizens must contribute $1,000 to the dam in order for it to be built. The dam, if built, is worth $70,000 to each citizen. 
-In the game in Scenario 13.7, the strategy pair that pays:
A) $69,000 to each player is the only equilibrium. 
B) ($0, -$1000) is the only equilibrium. 
C) (-$1000, $0) is the only equilibrium. 
D) $0 to each player is the only equilibrium. 
E) $69,000 to each player and the strategy pair that pays $0 to each player are equilibria.

Quizplus · Accepted Answer

In order for the dam to be built the citizens must contribute a total of $1,000,000 ($1,000 x 1,000 citizens). If every citizen contributes, the dam is built and each citizen receives $70,000, resulting in a total payoff of $69,000 for each citizen after their initial contribution of $1,000.

If a player chooses not to contribute, the dam will not be built and they will receive a payoff of $0. However, if all players choose not to contribute, the town will suffer from flooding and each player will receive a payoff of - $10,000 (representing the damages incurred by each person).

Therefore, the strategy pair that pays $69,000 to each player (if all players contribute) and the strategy pair that pays $0 to each player (if no player contributes) are equilibria. Thus, the correct answer is E.

Scenario 13.7 Consider the Game Below About Funding and Construction of a of a Dam