Chicken is a game played by two macho (i.e. somewhat stupid) teenagers who are attempting to prove who is the coolest (dumbest). Basically, they drive full speed at each other (head-on) on a narrow road and see who swerves first. The first to veer off is branded the chicken, whereas the one who doesn't swerve gains the esteem of the other teens. Of course, if neither veers, then they both die in the resulting crash. The payoffs for the Chicken game are as follows: (12 Marks)

Teen B

Veer Don't Veer

Teen A Veer 2, 2 1, 3

Don't Veer 3, 1 0, 0

(a) Draw the extensive form. (2 Marks)

(b) Find the pure-strategy Nash equilibrium or equilibria. (2 Marks)

(c) Compute the mixed-strategy Nash equilibrium. As part of your answer, draw the best-response function diagram for the mixed strategies. (2 Marks)

(d) Suppose the game is played sequentially, with teen A moving first and committing to this action by throwing away the steering wheel. What are teen B's contingent strategies? Write down the normal and extensive forms for the sequential version of the game. (2 Marks)

(e) Using the normal form for the sequential version of the game, solve for the Nash equilibria. (2 Marks)

(f) Identify the proper sub-games in the extensive form for the sequential version of the game. Use backward induction to solve for the sub-game perfect equilibrium. Explain why the other Nash equilibria of the sequential game are "unreasonable."