8.3 The game of Chicken is played by two macho teens who speed toward each other on a single-lane road. The first to veer off is branded the chicken, whereas the one who does not veer gains peer-group esteem. Of course, if neither veers, both die in the resulting crash. Payoffs to the Chicken game are provided in the following table.

Teen 2 Veer Does not veer Teen 1 Veer 2, 2 1, 3 Does not veer 3, 1 0, 0

a. Draw the extensive form.

b. Find the pure-strategy Nash equilibrium or equilibria.

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

d. Suppose the game is played sequentially, with teen 1 moving first and committing to this action by throwing away the steering wheel. What are teen 2’s contingent strategies? Write down the normal and extensive forms for the sequential version of the game.

e. Using the normal form for the sequential version of the game, solve for the Nash equilibria.

f. Identify the proper subgames in the extensive form for the sequential version of the game. Use backward induction to solve for the subgame-perfect equilibrium. Explain why the other Nash equilibria of the sequential game are ‘‘unreasonable.’’