Buck's Bolts

Buck's Bolts has hired a machinist to turn blanks into bolts as they come off the rolling and cutting mill.  In a continuous process the steel is made and then rolled out into a cylindrical shape. The cylindrical blank is cut to length while still hot and then a hexagonal head is pressed onto it.  After it cools the blank is put in a lathe and the threads are turned onto it.  This last step is the job of the new machinist, Les Threads.

Since Les is a new employee the firm has to decide whether or not they should monitor him.  This is necessary since  Les can put in a hard effort or a lazy effort.  Of course, Les knows when he is being monitored.   The firm can pay Les either a high wage or a low wage.

In the first stage of the game the firm must decide whether or not they will monitor Les.  In the second stage the firm makes a decision about the wage to pay and Les decides on his work effort. These decisions are made simultaneously. The game tree and payoffs appear as follows.

The variable m is the cost to the firm of monitoring Les in the workplace.  The variable e is the disutility to Les of working hard.
1. What are the subgames?
2. What are the Nash equilibria in the post-monitor subgame?
3. What are the Nash equilibria in the post-no monitor subgame?
4. In the second stage of the game are there dominant strategy solutions or IEDS solutions?
5. Can you write out the stategic form of the game?
6. What are the Nash equilibria in the strategic form of the game?
7. What is the subgame perfect equilibrium?