Question 3 Time left 1:23:15 2 Warning: 3 Not yet answered In any circumstances, you are NOT allowed to take/capture screenshot of any question in full or part of this Test. eClass is keeping all activities in a log file. Finish attempt ... Marked out of 10.00 Question: P Flag . Please note that this problem has four parts (a, b, c, and d). question You may need to scroll the screen down, navigate left and right to see the whole problem. Clearly label your parts when answering. You are allowed Maximum of 3 Files for this problem. Must use a pen to answer. Must show work completely (including all calculations/steps). Failure to do so will result in a score of "0," even if your final answer is correct The following is based on a case in which Game Theory was used during the Second World War between country A and country B. Country B troops, located in Rabaul, a city in New Guinea considering moving the troops to Rae, another city in New Guinea. There are two routes, North (N) and South (S), from Rabaul to Rae. Country, A troops were preparing for the air force attacks to prevent Country B from moving its troops. Country A was wondering which route should be scouted more intensively. The weather of the South (S) route tended to be clear and had clear visibility; whereas the weather of the North (N) route tended to be unclear and had poor visibility due to squalls. The following is the pay-off table of Country A troops, which indicates the duration of days Country A troops can attack Country B troops. Countries A and B troops selected their strategies based on Maximin and Minimax strategies, respectively. Hence, for example, if countries A and B take strategy N and strategy S, respectively, countries A's payoff is 2 and countries B's payoff is -2. Country B N N 2.5 W N CO Country A S 1.5 (a) Would countries A and B select their strategies deterministically? "Yes" or "No" - If your answer is "Yes," please show the strategies that countries A and B select, respectively. - If your answer is "No," please write the reason in one sentence. For questions (b), (c), and (d), please read the following: nd S with probability p1 and p2, respectively.The following is based on a case in which Game Theory was used during the Second World War Time left 1:22:57 between country A and country B. Country B troops, located in Rabaul, a city in New Guinea, considering moving the troops to Rae, another city in New Guinea. There are two routes, North (N) and South (S), from Rabaul to Rae. Country, A troops were preparing for the air force attacks to prevent Country B from moving its troops. Country A was wondering which route should be scouted more intensively. The weather of the South (S) route tended to be clear and had clear visibility; whereas the weather of the North (N) route tended to be unclear and had poor visibility due to squalls. The following is the pay-off table of Country A troops, which indicates the duration of days Country A troops can attack Country B troops. Countries A and B troops selected their strategies based on Maximin and Minimax strategies, respectively. Hence, for example, if countries A and B take strategy N and strategy S, respectively, countries A's payoff is 2 and countries B's payoff is -2. Country B N W N CO Z Country A 2.5 S 1.5 (a) Would countries A and B select their strategies deterministically? "Yes" or "No" - If your answer is "Yes," please show the strategies that countries A and B select, respectively. - If your answer is "No," please write the reason in one sentence. For questions (b), (c), and (d), please read the following: Assume that Country A troops choose strategies N and S with probability p1 and p2, respectively; Country B troops choose strategies N and S with probability q1 and q2, respectively. (b) If country B selects strategies N and S with probability q1 and q2, respectively, then what is Country A's expected payoff? (c) For different ranges of the probability that Country A troops take strategy N, the probability that Country B troops should take strategy N is different. For each of the ranges of the probability that Country A troops take strategy N, answer the corresponding probability that Country B troops take strategy N and resultant Country A's expected payoff. (d) What are the optimal probabilities that Country A should scout Rout N and Rout S, respectively