Question

1. It’s been estimated that if a truck collides with a car, the damage to the car one is A_C = $4,000. There is no damage to the truck. The probability of a collision is described by p(s_T, s_C) = (s_T²+ s_C²)/100,000, where s_T is the truck speed and s_C is the car speed, in km/h. The maximum speed the vehicles are capable of is 100 km/h.

Each driver can take precautions; assume the only feasible precaution is to reduce the speed. The cost of taking precautions by the truck driver is 4×(100 – s_T), that is the truck driver loses $4 value for every 1 km/h slowing down. The cost of taking precautions by the truck driver is 3×(100 – s_C), that is the car driver loses $3 value for every 1 km/h slowing down.

1. What are the efficient speeds by each driver? How often do collisions happen (i.e., what is the probability of a collision p) at the efficient speeds?

2. Suppose the rule is no liability = nobody compensates anyone else for the damages, in case of an accident. What speed would the truck driver choose? What speed would the car driver choose? How often do collisions happen (i.e., what is the probability of a collision p) at these chosen speeds?

Answer 1