5. [10 pts] Consider the following congestion game with four destinations: A, B. C, and D. - The road between A and B costs 3 for one driver to use and 6 per driver if two drivers use it. - The road between A and D costs 1 for one driver to use and 5 per driver if two drivers use it. - The road between B and C costs 1 for one driver to use and 2 per driver if two drivers use it. - The road between C and D costs 2 for one driver to use and 4 per driver if two drivers use it. All these roads can be taken in either direction. No roads connect A to C or B to D directly. Suppose Alice wants to get from A to C and Bob wants to get from B to D. Write this game between Alice and Bob in matrix form and find all the pure Nash equilibria. This corresponds to the situation from Footloose that we watched in class, where Kevin Bacon's character tries to swerve, but his shoelace randomly gets stuck, so is strategy is switched to drive. "Since this is a potential game, we know at least one such equilibrium exists