Economic - Game Theory

4. Consider the game of Chicken that we discussed in class: Two players, James and Dean, each has two strategies: Swerve and Straight. If they both choose Swerve, both get 0 as payoff. If they both choose Straight, both get -2 as payoff. If one chooses Swerve, the other chooses Straight, then the player chooses Straight gets 1 and the player chooses Swerve gets -1. a. Assume the game of Chicken is played sequentially with James moves first, and Dean moves second. Draw the game tree for this sequential game. Finding the rollback equilibrium of this sequential game. (5pt) b. Again, assume the game of Chicken is played sequentially with James moves first, and Dean moves second. Draw the payoff table for this sequential game. Finding the Nash equilibria of this sequential game. Are rollback equilibrium and Nash equilibria the same? If not, why? (5pt)