4. Consider the game of chicken. Two players drive their cars down the center of the road directly at each other. Each player chooses SWERVE or STAY. Staying wins you the admiration of your peers (a big payoff) only if the other player swerves. Swerving loses face if the other player stays. However, clearly, the worst output is for both players to stay! Specifically, consider the following payouts. Player two Stay swervePlayer one stay -6 -6 2 -2 swerve -2 2 1 1Does either player have a dominant strategy?

Complete question:

Consider the game of chicken. Two players drive their cars down the center of the road directly at each other. Each player chooses SWERVE or STAY. Staying wins you the admiration of your peers (a big payoff) only if the other player swerves. Swerving loses face if the other player stays. However, clearly, the worst output is for both players to stay! Specifically, consider the following payouts. Player two Stay swervePlayer one stay -6 -6 2 -2 swerve -2 2 1 1

a) Does either player have a dominant strategy?

b) Suppose that Player B has adopted the strategy of Staying 1/5 of the time and  swerving 4/5 of the time. Show that Player A is indifferent between swerving and staying.

c) If both player A and Player B use this probability mix, what is the chance that  they crash?

Explanation:

a. There is no dominant strategy for either player. Suppose two players agree to live. Then the best answer for the player is to swerve(-6 versus -2).  Yet if the player turns two, the player will remain one (2 vs 1).  

b. Player B must be shown to be indifferent among swerving and staying if it implements a policy (stay= 1⁄4, swerving= 5/4).

When we quantify a predicted award on the stay / swerving of Player A, we get

E(stay)= (1/5)(-6)+ (4/5)(2)= 2/5 E(swerve)= (1/5)(-2)  

c. They both remain 1/5 of the time. The risk of a crash (rest, stay) is therefore (1/5)(1/5)= 1/25= 4%

steering wheels are always situated on the left side of the car.

always drive on the right side of the road.

white lines separate lanes of traffic traveling the same direction.

hashed or broken lines means you may change lanes when it is safe.

solid white lines mean stay in your lane.

yellow lines separate traffic moving in opposing directions.

hashed or broken yellow lines mean you can carefully pass, paying attention to oncoming traffic.

never cross a solid yellow line (or double yellow line).

when turning left at an intersection, pass in front of any cars that are turning left from the opposing direction (do not try to pass behind them).

use the left lane to pass other cars traveling your direction.

do not pass in the right lane unless absolutely necessary.

if you are driving in the far left hand lane and someone would like to pass you, move over to the right lane when it is safe to do so and allow them to pass.

you must always yield to pedestrians.

come to a complete stop whenever you see pedestrians trying to cross the street.

never pass a school bus if it has flashing red lights. wait until the lights have stopped.

be aware of bicyclists. often they share the road with cars and are supposed to also follow general traffic laws.

be particularly careful about driving in cities with bike lanes -- always check before turning that a bike is not coming.

it is mandatory to pull over or stop at an intersection to allow an emergency vehicle to pass you if you see one traveling with lights flashing and/or a siren running.

do not overuse your car horn. horns are used almost exclusively for emergency situations or for when you feel unsafe.

explanation: