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

Exercise 14

Refer back to Chapter 5, in particular to the Battle of the Sexes in Table Imagine that these payoffs are monetary payoffs.
a. Suppose that players only care about monetary payoffs, with $1 - 1 util. What are the pure-strategy Nash equilibria?
b. Suppose that players have extreme preferences for fairness. Each player loses 10 utils for each dollar difference (in absolute value) between their payoffs. Show how the payoffs in the Battle of the Sexes 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. Now only the player who earns more money cares about fairness. This player feels guilty about earning more, losing 10 utils for each dollar advantage. Write down the normal form of the Battle of the Sexes reflecting these new preferences. Find the pure-strategy Nash equilibria.
Table Battle of the Sexes in Normal Form