Intermediate Microeconomics and Its Application 12th Edition by Walter Nicholson,Christopher Snyder

Exercise 8

Refer back to Chapter 5, in particular to the Prisoners' Dilemma in Figure. Imagine that these payoffs are monetary payoffs, with negative numbers being money that is taken away from a player.
a. Suppose that players only care about monetary payoffs, with $1 - 1 util. Find the pure-strategy Nash equilibria.
b. Suppose that players have a preference for fairness. Each player loses 1 util for each dollar difference (in absolute value) between their payoffs. Show how the Prisoners' Dilemma payoffs would change by writing down a new normal form. Find the pure-strategy Nash equilibria.
c. Suppose that players have different fairness preferences than in part b. Suppose that only the player who earns less money cares about fairness. That player loses 1 util for each dollar less he or she earns than the other player. Write down the normal form of the Prisoners' Dilemma reflecting these new preferences. Find the pure-strategy Nash equilibria.
Figure Prisoner's Dilemma in Extensive From