Game Theory 9. Imagine two drivers, Driver I and Driver II, are driving on a rainy night in opposite directions. There is a narrow bridge in front of the two drivers. The bridge is so narrow that both drivers know that only one vehicle can cross the bridge at a time. The drivers can barely see what's on the other side of the bridge, but a gleam of light tells each of them there's another driver on the other side of the bridge facing the same dilemma. Now let's suppose if both of the drivers choose to drive onto the bridge then both drivers will get stuck in the middle, which is the worst scenario for both drivers. Each driver will spend 5 minutes backing up to get off the bridge and arrange for who will travel across the bridge first. On the other hand if one of the drivers chooses to wait while the other one chooses to drive onto the bridge, then the one who drives first across the bridge will gain two minutes on their drive while the driver who has to wait will only lose a minute waiting. If both drivers decide to wait then they will both lose ten minutes time trying to figure out what to do. Assume that both drivers seek to minimize their additional travel time. The detailed payoff matrix is listed below: Driver II Travel Across Bridge Wait Driver I Travel Across Bridge ((-5,-5) (2,-1) Wait (-1,2) -10,-10) a. Is the choice of both drivers choosing to wait an equilibrium? Explain your answer. b. Is there any strictly dominant strategy for Driver I? c. What is your prediction for the equilibrium outcome of this game? Suppose you saw that the driver on the other side of the bridge is your uncle who is a well- known slow tempo person. He also sees you. So, effectively you are now Driver I and your Uncle is Driver II. You understand your Uncle is always going to wait in this kind of situation so the payoff matrix now becomes: Driver II: Your Uncle Travel Across Wait Driver I: You Travel Across (-5,-5) (2,3) Wait (-1,2) (0,3) d. Is there a strictly dominant strategy for your uncle? e. What is your prediction for the equilibrium to this game now