Judith Serrato Sec. 1F 14 May 2019 Homework #4 Question 1 Game A Left Right Top 0 0 -1 2 Bottom 3 -1 4 4 Q(0) + (1-Q) 3 = Q(-1) + (1-Q) 4 Q=1/2 P(0) +(1-P) -1 = P(2) + (1-P) 4 NO MSNE P= 5/3 Game B Left Right Top -1 2 2 3 Bottom 0 1 2 1 Q(-1) + (1-Q) 0 = Q(2) + (1-Q) 2 NO MSNE Q= -2 Game C Left Q= ¾ Right 1-Q = P= 2/5 Top 0 3 -1 0 1-P= 3/5 Bottom -1 2 2 4 MSNE: Q= ¾ P= 2/5Game D Left Q= 1/2 Right 1-Q =1/2 P= 3/5 Top 1 0 6 2 1-P= 2/5 Bottom 5 4 0 1 MSNE: q= ½ , P=3/5 Game E Left Q = 2/5 Right 1 – Q = 3/5 P= 2/3 Top 0 0 3 -1 1-P= 1/3 Bottom 3 -1 1 1 MSNE q= 2/5, P= 2/3 Question 2 Technical Skills II-A-1 Strike Q = 4/9 Not 1 – Q = 5/9 P= 7/12 Restrict -4 3 1 -2 1-P= 5/12 Not 4 -7 0 0 II-A-2 There are no pure strategy equilibriums because the actions of the players would be random and could not be one concise thing. II-A-3 MSNE: q= 4/9, p= 7/12 28/108 prob. of gov. restricting, terrorist striking 35/108 prob. of gov. restricting, terrorists not striking 20/108 prob of gov. not restricting, terrorists striking 25/108 prob. gov. not restricting, terrorists not striking 3/10 2/10 3/10 2/10 4/15 2/15 6/15 3/15 28/108 20/108 35/108 25/108Interpretation II-A-4 The probability of a successful strike by the terrorists would be 20/108 (5/27th) which is the lowest probability of all the potential outcomes in this situation. The probability of an unsuccessful attack would be 28/108 (7/27) which is lower than the probability of the terrorists not striking and the government still restricting individuals of their rights. Technical Skills II-B-1 Strike Q = 2/5 Not 1 – Q = 3/5 P= 7/12 Restrict -5 3 1 -2 1-P= 5/12 Not 4 -7 0 0 II-B-2 There is still no pure strategy Nash equilibrium. Changing -4 to -5 was not of huge effect into strategies. II-B-3 MSNE: q=2/5, p=7/12 Interpretation II-B-4 The highest predicted outcome is that the terrorists do not strike and the government still tries to play it safe by restricting citizens. The probability of this; however, is not high enough to assume that this may be the sole outcome of the situation. The probability of a successful strike would be 1/6th and the probability of the not striking at all is 36/60 (3/5th). II-B-5 The probability decreases because it is not the outcome the way would want to occur. II-B-6 14/60 10/60 21/60