many areas of the country, aquifers (pools of underground water) serve as the primary water source. Water is extracted from the aquifer using wells and is replenished by rain and rivers. In many places the water is being extracted from the aquifers faster than it is being replenished, causing wells to run dry and farmers to have insufficient water for their crops. To address this, farmers in Kansas have all mutually agreed to reduce their usage of water. After reaching this agreement, each farmer must decide whether to follow the agreement. Assume that if everyone chooses a low level of production, all farmers will have enough water for the entire season. If a farmer chooses a high level of production, they will have more crops to sell but it will reduce the water available (and therefore the crop quality) for all farmers. Specifically, the farmers are faced with the decision shown in the images. a. If the game is played only one time, characterize each farmer’s best strategy. b. What is the Nash equilibrium? Is the Nash equilibrium pareto efficient? Briefly explain why or why not. c. If this were an infinitely repeated game, what outcome would you expect to emerge as the equilibrium? Briefly explain.

3. many areas of the country, aquifers (pools of underground water) serve as the primary water source. Water is extracted from the aquifer using wells and is replenished by rain and rivers. In many places the water is being extracted from the aquifers faster than it is being replenished, causing wells to run dry and farmers to have insufficient water for their crops. To address this, farmers in Kansas have all mutually agreed to reduce their usage of water. After reaching this agreement, each farmer must decide whether to follow the agreement.

Assume that if everyone chooses a low level of production, all farmers will have enough water for the entire season. If a farmer chooses a high level of production, they will have more crops to sell but it will reduce the water available (and therefore the crop quality) for all farmers. Specifically, the farmers are faced with the decision shown in the images.

a. If the game is played only one time, characterize each farmer’s best strategy.
b. What is the Nash equilibrium? Is the Nash equilibrium pareto efficient? Briefly explain why or why not.
c. If this were an infinitely repeated game, what outcome would you expect to emerge as the equilibrium? Briefly explain.