Returning from a remote island, Lucy and Pete, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it. Instead he asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty-the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44. What numbers will Lucy and Pete write? What number would you write?Exercise 4. [1 point] Recall Traveller's Dilemma from the Welcome Video. Consider a slight variation of the game where the airline manager asks Lucy to say a number first and Pete can go next. Pete will know what Lucy says when he states the price of the gift. Assume both Pete and Lucy are interested in maximizing just their own payoffs. . What number will Lucy say? What about Pete? What will Lucy and Pete get? Briefly explain your response to (i) and (ii). [Hint: One way to think about it is that suppose Lucy says L e (2, 3, ..., 100). What is Pete's best response? Anticipating that what will Lucy say.]