Question 15.47

15. You have the choice of either parking illegally on the street or parking in the lot and paying $16. Parking illegally is free if the police officer is not patrolling, but you receive a $40 parking ticket if she is. However, you are peeved when you pay to park in the lot on days when the officer does not patrol, and you are willing to assess this outcome as costing $32 ($16 for parking plus $16 for your time, inconvenience, and grief). It seems reasonable to assume that the police officer ranks her preferences in the order (1) giving you a ticket, (2) not patrolling with you parked in the lot, (3) patrolling with you in the lot, and (4) not patrolling with you parked illegally.

  1. Describe this as a matrix game, assuming that you are playing a zero-sum game with the officer.
  2. Solve this matrix game for its optimal mixed strategies and its value.
  3. image Discuss whether it is reasonable or not to HÉP assume that this game is zero-sum.
  4. Assuming that you play this parking game each working day of the year, how do you implement an optimal mixed strategy?

15.

(a)

Officer Does Not Patrol Officer Patrols
You park in street 0 −$40
You park in lot −$32 −$16

(b) Your optimal mixed strategy: ; officer’s optimal mixed strategy: ; value: −$22.86

(c) It is unlikely that the officer’s payoffs are the opposite of yours.

(d) Answers will vary.