3: 20% Consider the Battle of Hoth in the Star Wars movie. Luke Skywalker (player 1) has to return to and help defend the Echo Base against the attack by Galactic Empire (the enemy). He needs to choose one of the four routes, a, b, c or d (listed in order of speed in good conditions). Fast routes are more likely to be struck by a snow slide. At the same time, the Darth Vader (player 2), his rival, has to choose whether to sacrifice (y) or not to sacrifice (x) his valuable battle vehicle, AT-AT, to cause a snow slide. The payoffs of this game are represented here: Darth Vader (player 2) x y a 12,0 0,6 Luke Skywalker (player 1) b 11, 1 1,5 C 10, 2 4,2 d 9,3 6,0 a. Let q denote the probability that the Darth Vader (player 2) selects x. Draw the diagram of Luke Skywalker's (player 1's) expected payoff of each pure strategy with respect to q. Use this diagram to explain what Luke should do if q>2/3, if q <2>