Problem 3. Val and Earl are at work on a very hot afternoon. There is a job waiting for them. It takes only one person to do the job. The one who does it must crawl through a mucky culvert to connect a pipe. Once the pipe is connected, they can both go to a comfortable tavern for a beer. The game tree is shown below, where at the terminal nodes, the top number is Val's payoff and the bottom number is Earl's payoff. Val Do it Stall V 5 E 10 Earl Do it Stall 9 Val 4 Do it Stall 38 Earl Do it Stall 7 Val Do it Stall Earl 110 Do it Leave it 5 0 X X At the beginning of play, Earl is working on another job, but Val could do the job and if he does it right away, they can both go out for beer. Val could choose to stall, waiting for Earl to come back. If Val decides to stall, then when Earl gets back, he could do the job, or he could stall. If Earl chooses to stall, Val could either do the job, or stall again, and so on... If Val and Earl both stall until Earl's final decision node at the end of the workday, Earl can either do the job, or they can both leave the job undone. The payoffs to both from leaving the job undone are given by the variable X. C) Find the subgame perfect Nash equilibrium profile if X < 0. In this equilibrium, who if anyone, does the job? Explain your answer. D) Find the subgame perfect Nash equilibrium profile if 0 < x < 1. In this equilibrium, who if anyone, does the job? Explain your answer. E) Find the subgame perfect Nash equilibrium profile if 1 < X < 2. In this equilibrium, who if anyone, does the job? Explain your answer. Exercise 2. 1. How could they do that! They abducted Speedy, your favorite tortoise! They asked for $1,000 in unmarked bills and threatened to kill Speedy if you don't pay. Call the tortoise-napper Mr. T. Let the possible outcomes be as follows: o, you don't pay and speedy is released 02: you pay $1,000 and speedy is released 03: you don't pay and speedy is killed 04: you pay $1,000 and speedy is killed You are attached to Speedy and would be willing to pay $1,000 to get it back. However, you also like your money and you prefer not to pay, conditional on the two separate events "Speedy is released" and "Speedy is killed": your ranking of the outcomes is 0₁ > 04. On the other hand, you you you 03 you are not quite sure of what Mr. T's ranking is. (a) Suppose first that Mr T has communicated that he wants you to go to Central Park tomorrow at 10:00am and leave the money in a garbage can; he also said that, two miles to the East and at the exact same time, he will free Speedy in front of the police station and then go and collect his money in Central Park. What should you do? (b) Suppose that Mr T is not as dumb as in part (a) and he instead gives you the following instructions: first you leave the money in a garbage can in Central Park and then he will go there to collect the money. He also told you that if you left the money there then he will free Speedy, otherwise he will kill it. Draw an extensive form or frame to represent this situation.