Game Theory

Assume you are in the market for a luxury car. You encounter your salesperson "Brian", who is

excited to see you and help you make this important purchase. You have not decided on a new

or used car at this point. Brian recommends a used car that is currently available on the lot at

his dealership. You also saw a comparable model on Cars.com that was brand new at another

dealership that is an hour away. As you are sitting at Brian's desk, he offers you a nice cold

beverage and a snack. Although you have indicated that you may also like to go see the other

car, Brian recommends running your credit to see how low of an interest rate he can get you.

This seems to take some time, and at this point 2 hours has gone by. After running your credit,

Brian further recommends that you speak with the finance manager about additional

accessories and after-market options available. Now 4 hours has gone by and you

communicate that although everything sounds really good about the car, you are concerned

about the condition of buying a used car. Brian then offers to discount the extended warranty

on the car by 25% in order to earn your business. It is now 30 minutes before 6:00pm, the time

in which all dealerships close within a 2hr drive.

Question:

please create a diagram with a 2x2 matrix to explain possible scenarios

and payoffs using the scenario above. Is there a Nash Equilibrium possible in your

scenario? If so explain, If not explain.