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 $5. Carrying the pails of water down requires considerable effort. Both Jill and Jack would be willing to pay $4 each to avoid carrying one pail down the hill, and an additional $4 to avoid carrying a second pail down the hill.

a. Given market prices, how many pails of water will each child fetch from the top of the hill?

pails.

b. Jill and Jack

a) Each player’s payoffs are independent of the action taken by the other. Each pail of water sells for $6. Cost of carrying on bucket is 4 and another bucket is 5. Since the cost of carrying each bucket is less than $6. Both, Jill and Jack will each carry 2 buckets.

b. Now, Jack and Jill are sharing their revenues. They will try to maximise their payoff. The payoff matrix will be as below:

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.