Question

Jill and Jack both have two pails that can be used to carry water down from a hill. Each makes only one trip down the hill, and each pail of water can be sold for $4. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $2 each to avoid carrying one pail down the hill, and an additional $3 to avoid carrying a second pail down the hill.

a. If Jack and Jill each must decide whether to carry one or two pails of water down from the top of the hill, how many pails will each child choose to carry?

b. Jill and Jack’s parents are worried that the two children don’t cooperate enough with one another. Suppose they make Jill and Jack share equally their revenues from selling the water. Given that both are self-interested, construct the payoff matrix for the decisions Jill and Jack face regarding the number of pails of water each should carry.

Answer 1

Payoff Calculation:

Jack and Jill both carry 1 pail, that is, 2 pails in total:

Jack payoff= total revenue/2 – cost of carrying down the pail = $6(2)/2 - $4(1) = $2

Jill Payoff= total revenue/2 – cost of carrying down the pail = $6(2)/2 - $4(1) = $2

Jack carries 2 pails, Jill carries 1 pail, that is, 3 pails in total:

Jack payoff: total revenue/2 – (cost of carrying on the first pail + cost of carrying second pail)

= $6(3)/2 - $4(1) - $5(1) = 9 -9 =$0

Jill payoff: total revenue/2 – cost of carrying on the first pail

= $6(3)/2 - $4(1) =$5

Jack carries 1 pail, Jill carries 2 pails, that is, 3 pails in total:

Jack payoff: total revenue/2 – cost of carrying on the first pail

= $6(3)/2 - $4(1) =$5

Jill payoff: total revenue/2 – (cost of carrying on the first pail + cost of carrying second pail)

= $6(3)/2 - $4(1) - $5(1) = $0

Jack and Jill both carry 2 pails, that is, 4 pails in total:

Jack payoff: total revenue/2 – (cost of carrying on the first pail + cost of carrying second pail)

= $6(4)/2 - $4(1) - $5(1) = 12- 9 = $3

Jill payoff: total revenue/2 – (cost of carrying on the first pail + cost of carrying second pail)

= $6(4)/2 - $4(1) - $5(1) = 12- 9 = $3

This game is a like prisoners’ dilemma. Because, if Jack choose to carry 1 pail the better response from Jill is to carry 1 pail because he will get better payoff of 2. If Jack choose to carry 2 pail the better response from Jill is to carry 1 pail because he will get better payoff of 5. So, for Jill carrying 1 pail is dominant strategy.

Same ways, if Jill choose to carry 1 pail the better response from Jack is to carry 1 pail because he will get better payoff of 2. If Jill choose to carry 2 pail the better response from Jack is to carry 1 pail because he will get better payoff of 5. So, for Jack carrying 1 pail is dominant strategy.

For both Jack and Jill, the dominant strategy is to carry only one bucket down the hill.

Step-by-step explanation: