2)Consider an example from car-racing. Two drivers are approaching a corner of the track. They each have the option to drive aggressively or cautiously. Driving aggressively gives each driver the better chance of getting ahead, but if both drive aggressively into the corner, there is a significant possibility of a crash. The payoffs are as follows:

Driver 1\ Driver 2

Drive Aggressively

Drive Cautiously

Drive Aggressively

-10, -10

80, 10

Drive Cautiously

10, 80

40, 40

a.Does either player have a dominant strategy? Explain.

b.What are the Nash equilibria of this game? Explain.

Part B - Zero-Sum Games

3)Assume that on a penalty kick in soccer, the shooter can choose to shoot left or right, and the goalie can dive to the shooter's left or right. The expected payoffs for each combination of choices is given in the table (payoff's to the .

Dive toShooter's Left

Dive to Shooter's Right

Shoot Left

75%, 25%

95%, 5%

Shoot Right

90%, 10%

65%, 35%

a.Does either player have a dominant strategy? Explain.

b.Is there a pure strategy Nash equilibrium to this game? Explain.

c.What is the Nash equilibrium of this game?

d.In the Nash equilibrium, what is the likelihood of scoring a goal if the shooter shoot's left? If they shoot right?

Part C - Sequential Games

4)A game involves two players. There are five sticks in the middle. On each player's turn, they can pick up one or two sticks. The winner of the game is the player that picks up the last stick.

a.Explain how you can solve this game using backwards induction.

b.What is the Nash equilibrium outcome of the game?

c.Now the game starts with six sticks in the middle. How does that change the Nash equilibrium? Explain.