Q3 On Her Majesty's Secret Service The famous British spy {107 has to choose one of four routes A, B, C, or D (listed in order of speed in good conditions] to ski down a mountain. Fast routes are more susceptible to an avalanche. At the same time, the notorious rival spy 001 has to choose whether to use Y or not to use X his valuable explosive to try to cause an avalanche to undermine 007's success. The payoffs to this game are as follows: 007 A 13 e D Km Y an 5,1 2,4 0,6 001 (a) Suppose that 001 choses to not use the explosives (i.e.1 chooses X] with probability p where {l g p 5 1 and choses to use the explosives (i.e., chooses Y) with probability 1 p. What will 007 do when p %. (Hint: construct the best response of {107 Bitumen (b) Suppose that you are Q, the famous technical advisor to MI. Are there any routes you would advise {107 certainly not to take? Explain your answer. ((3) The gripped viewer of this epic drama is trying to gure out what will happen. Find a Nash equilibrium in which one player plays a pure strategy and the other player plays a mixed strategy. (d) Now nd a di'erent mixedstrategy equilibrium in which the pure strategy from the equi librium identied in part (c) is assigned zero weight