Jack and Jill are arrested and charged with theft of water supplies.The police suspect that Jack and Jill have taken water from a private well, but do not have enough evidence to make the theft charge stick. But they can be charged with a lesser crime. The district attorney separates them and offers them a deal. Spending fewer days in jail is preferred to more days in jail.

a.Jack only cares about the time he spends in jail and Jill only cares about the time she spends in jail. Can we predict what each will do?What is the equilibrium? Explain.

b.Suppose Jack cares how many days Jill spends in jail and, likewise, Jill cares how many days Jack spends in jail. Let their payoff (or penalty) be the sum of the days the two spend in jail, combined. What is the equilibrium given this altruism?

c.Like (b), each cares about the other's time in jail, but to a lesser extent than their own time in jail. Let each person's payoff be their days in jail + W*the other's days in jail, where W is less than 1.0. If W = 0.2, what is the equilibrium or equilibriums? (Show your work.)