(A simple model of monitoring.) A company consists of two kinds of employees, tall and short. Each person can work in either of two jobs, honest work or stealing from the company. The wage to honest work for a short person is wS, while the wage for a tall person is wT. Whichever job she chooses, each person reports to a boss. The boss sees the person's height, but not her job. The boss has to decide whether or not to stop the person and inspect her work. For simplicity, think of this as two games, one between the tall person and the boss and one between the short person and the boss.The payoffs to the person and the boss are as follows (where the person is player 1 and the boss is player 2):
Inspect Don't inspect
Steal 0, 10 10, 0
Honest Work wi-5, 4 wi, 5
Assumptions: wS < wT. Stealing from the company is very profitable, so wT < 10. Finally, honest work is better than stealing from the company, even if the boss inspects the honest person. That is, 5 < wS.
Find all Nash equilibria in pure and mixed strategies for the game between the short p?dun and the boss and for the game between the tall person and the boss. Compare the likelihood of a short person being inspected to the likelihood of a tall person being inspected. Also, compare the probability a short person steals from the company to the probability a tall person does so. Compare the wage difference wT - wS to the difference in equilibrium payoffs between the two types.