Yi Y2, Y: > 0 By considering that Yi = 0; Y2 = 0; Y3 = 0.020: Y1 + y2 + Y3 = 1/-- = 50 - V= 0; 91 = Y, n=0 92 = Yu=0 q3 = 13 1= 1 The optimal strategy for George is to always pass. 8.11 Security Measures to Avoid Snipers m24 The secret security services protecting the First Lady in the USA have received a warning from a sniper, who is posted in the surroundings of a public school where the First Lady is giving a speech. The security guards can choose from among five cars which drive one behind the other (1, 2, 3, 4 or 5) to transport the First Lady (Fig. 8.4). The sniper will shoot only once from any of the four spots A, B, C or D. A shot would harm the First Lady if she travelled in a car next to the place where the bullet was shot, For instance, a bullet shot from point A would harm the First Lady if she travelled in ear 1 or 2. while a bullet shot at point D would harm whoever is in car 4 or 5. Let us assume that the sniper would be offered award 1 if the First Lady was harmed and 0 if she was unhurt. (a) By assuming that this is a zero-sum game, consider the payoff matrix from the sniper's viewpoint (b) Find and eliminate all the dominated strategies. (e) We are informed that an optimal strategy for the security guards is that the First Lady travels one third of the times in cars 1, 3 and 5. We are also told that an optimal strategy for the sniper is to shoot one third of the times to point A, one third to D and one third to B or C. Determine the game value for the sniper. DAS 2 B 3 C 4 D 5 Fig. 8.4 How the cars are arranged to avoid a sniper 8.11 Security Measures to Avoid Snipers 301