2. Jack and Jill decided to go camping in the winter. Both Jack and Jill need to collect firewood to light a fire to keep themselves warm at night. Both can decide to collect firewood or instead shirk their responsibilities. If both collect firewood, then both can stay warm at night. If one person collects and the other one doesn’t then the person who shirks will not have to put in the effort to collect firewood but will get to enjoy the warmth of the fire. If both shirk then both stay cold at night. The following table represents the Jack’s and Jill’s payoffs in each scenario:

a) Find all Nash equilibria assuming each maximizes their own payoffs.

b) Suppose both Jack and Jill like each other and have non-standard preferences with u(x1, x2) = (x1 + 0.5 x2), where x1 is the own payoff, while x2 is the payoff for the other person. What is the Nash prediction under these preferences? Explain.

c) Suppose both Jack and Jill have competitive preferences and care only about how much better or worse off they are compared to each other. In other words, u(x1 , x2) = (x1 - x2) for both. What is the Nash prediction now? Explain.

d) Suppose both Jack and Jill are inequality averse and lose half a unit of utility for each unit difference in payoffs. In other words u(x1 , x2) = x1 – 0.5 (|x1 - x2|). Find all Nash equilibria and explain.