Name

A. This is a game depicting the market for mainframe computers in the late 1960’s.  IBM is the incumbent and Telex is thinking of entering the market with its own plug-and-play components.  If Telex stays out then it is profitable in another market niche.  If Telex enters then IBM can either smash Telex by cutting prices to the bone or accommodate.  The payoffs of either action are shown. 

1. How many subgames are there in this game?
2. Solving the game using rollback induction, Telex will play    and IBM will play .
3. On a separate peice of paper, write out the normal form of the game.  There are two pure strategy Nash equilibria in the normal form of the game. What are they? Enter your answers in the appropriate boxes.

4. Do all of the Nash equilibria you identified in the previous part involve credible strategies? Enter the non-credible strategic profiles in the appropriate boxes.

B. Chicken: James and Dean are playing Chicken.  They drive toward each other at a high rate of speed.  The driver that swerves first is deemed a chicken and loses face with the rest of the in-crowd.  The simultaneous move game with payoffs is depicted below.

5. What is/are the Nash equilibrium in this normal form of the game?

6.  On a separate piece of paper write out the extensive form of the game when play is sequential and James goes first. How many subgames are there?

7. What is the solution to the game that you have just drawn?

8. On a separate piece of paper write out the extensive form of the game when play is sequential and Dean goes first. How may subgames are there?

9. What is the solution to the second version of the extensive game that you have just drawn?

If you look at the two extensive forms of the game James - Dean game that you drew you will see that each them contains both of the Nash equilibria that you found in the Normal form of the game.  But, when you solved each of the extensive form games there was a unique solution in each. 

10. We can attribute the uniqueness of the solutions in the extensive forms to Zermelo's Theorem.  True  False

11. In each of the extensive forms of the James - Dean game the solution that you found can be said to be a subgame perfect equilibrium.  True  False

You should be able to explain your answer to 11 in class.