2. (14 pts) The fraud game Warning: This game is purely for educational purposes and does not condone fraud of any kind. A train traveler named Mark can pay a train ticket or attempt to ride the train for free. If Mark is caught, he must pay a hefty fine. For the train company, checking a traveler's ticket costs money. The game parameters are as follows: . P : the ticket price . c : the cost of checking a traveler's ticket . F : the fine which must be paid by a traveler caught without a ticket Note: F > P > c. a) (2 pts) Fill in the following normal-form game with the appropriate numbers The train company Checks ticket Does not check ticket Mark Buys a ticket Does not buy a ticket b) (4 pts) Is there a pure-strategy Nash equilibrium? What is it? (Or explain why there is none). c) (4 pts) Assume Mark buys his ticket with probability p and the train company checks tickets with probability q. Find the mixed-strategy Nash equilibrium. d) (4 pts) The train company is considering lowering the price of the ticket to reduce fraud. What will happen to the fraud level if i) It still checks with the same probability q? ii) It adjusts its probability q? Comment