The chief executive officer of a firm in a highly competitive industry believes that one of her key employees is providing confidential information to the competition. She is 85% certain that the informer is the Vice President (VP) of Information Technology, whose knowledge has been extremely valuable in their data analysis. Assume that he would certainly lie about this when confronted if he is indeed the informer (in other words the probability that he would lie is the same as the CEO's suspicion probability). If she decides to fire this VP and he is the informer, she estimates that the company will gain $8.2 million. If she decides to fire this VP but he is not the informer, the company will lose his expertise and he might sue them, as well she will still have an informer on staff, the CEO estimates that this outcome would cost her company about $13 million. If she decides not to fire this VP, she estimates that the firm will lose $5.4 million regardless of whether he actually is the informer (because in either case the informer is still within the company). Before deciding whether to fire the VP, the CEO could order one of two different lie detector tests. To avoid possible lawsuits, the lie detector tests would have to be administered to all company employees, at a total cost of $285,000 for Lie Detector Test 1 and $975,000 for Lie Detector Test 2. Lie Detector Test 1 is not perfectly reliable: if a person is lying, this test will reveal that the person is lying 96% of the time and, if a person is not lying, this test will indicate that the person is not lying 92% of the time. Lie Detector Test 2 is 100% reliable (perfect!). Note that although the original problem was done using software, you must solve this with Excel as the formulas have been erased. Just use full $ values (no cents). Watch for negative values! a) On the decision tree template: i. At the top of the worksheet calculate the Bayes probabilities. Reference the final values in your decision tree in the proper cell (which will be the non- rounded value) ii. Calculate the values at each node (in blue). Put the probabilities on top of the branch description (yellow highlights). Use full numbers. You do not have to show the intermediate values for the branches, just the terminal node values. Prune all of the branches that are not needed. iv. Highlight the entire optimal strategy (by choosing the branches (mouse click) and then Format Shape Effects Glow). b) What strategy should the CEO adopt to minimize the expected total cost of managing this difficult situation? State the optimal strategy in words including all steps and the final EMV. A B C D E F H 1 K L M N 0 P Q R s T U 1 2 NI is Non-Informer Inf is Informer P(Inf) = PINI) = Lie Detector 1 Pl+ | Inf) = PC- Inf) = 3 Savings: Fire and he is Informer $8,200,000 4 Cost: Fire and he is NOT Informer $13,000,000 5 Cost: Do Not Fire VP -$5,400,000 6 Cost Lie Detector 1 1 $285,000 7 Cost Lie Detector 2 $975,000 8 9 The "yellow" cells have probabilities and 10 the "blue" cells have node values. 11 You can use this prune in your tree: 12 The best strategy is to 13 14 Pl+ NI) = PC- INI) = Bayes: P(+) = P(+ | Inf) * P(Inf) + P(+NI) * P(NI) = P(Inf | +) = P(+ | Inf) * P(Inf) /P(+) = 15 PINI |-) = P(- | NI) * P(NI)/P(-) = Is Informer 16 17 18 19 20 21 22 23 $7,915,000 Fire VP A B C D E F H 1 1 J K L M N o P R S s T U V w Y Z Q Is Informer $7,915,000 Fire VP Is Not Informer Positive Result (Lying) Do Not Fire VP Use Lie Detector 1 o Is Informer Fire VP 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Is Not Informer Negative Result (Not Lying) Do Not Fire VP -$5,685,000 Is Informer Fire VP Is Not Informer Positive Result (Lying) 57 58 59 60 Do Not Fire VP A B D E F H K L M N O P Q R S T U 1 J Positive Result (Lying) Do Not Fire VP 55 56 57 58 58 59 60 4 61 62 63 64 65 66 67 68 69 Use "Perfect" Lie Detector 2 Is Informer Fire VP Is Not Informer Negative Result (Not Lying) Do Not Fire VP Is Informer Fire VP 70 71 72 73 74 75 76 77 78 79 80 31 82 83 84 85 36 87 88 89 90 91 92 92 93 94 95 Is Not Informer No Lie Detector $13,000,000 Do Not Fire VP The chief executive officer of a firm in a highly competitive industry believes that one of her key employees is providing confidential information to the competition. She is 85% certain that the informer is the Vice President (VP) of Information Technology, whose knowledge has been extremely valuable in their data analysis. Assume that he would certainly lie about this when confronted if he is indeed the informer (in other words the probability that he would lie is the same as the CEO's suspicion probability). If she decides to fire this VP and he is the informer, she estimates that the company will gain $8.2 million. If she decides to fire this VP but he is not the informer, the company will lose his expertise and he might sue them, as well she will still have an informer on staff, the CEO estimates that this outcome would cost her company about $13 million. If she decides not to fire this VP, she estimates that the firm will lose $5.4 million regardless of whether he actually is the informer (because in either case the informer is still within the company). Before deciding whether to fire the VP, the CEO could order one of two different lie detector tests. To avoid possible lawsuits, the lie detector tests would have to be administered to all company employees, at a total cost of $285,000 for Lie Detector Test 1 and $975,000 for Lie Detector Test 2. Lie Detector Test 1 is not perfectly reliable: if a person is lying, this test will reveal that the person is lying 96% of the time and, if a person is not lying, this test will indicate that the person is not lying 92% of the time. Lie Detector Test 2 is 100% reliable (perfect!). Note that although the original problem was done using software, you must solve this with Excel as the formulas have been erased. Just use full $ values (no cents). Watch for negative values! a) On the decision tree template: i. At the top of the worksheet calculate the Bayes probabilities. Reference the final values in your decision tree in the proper cell (which will be the non- rounded value) ii. Calculate the values at each node (in blue). Put the probabilities on top of the branch description (yellow highlights). Use full numbers. You do not have to show the intermediate values for the branches, just the terminal node values. Prune all of the branches that are not needed. iv. Highlight the entire optimal strategy (by choosing the branches (mouse click) and then Format Shape Effects Glow). b) What strategy should the CEO adopt to minimize the expected total cost of managing this difficult situation? State the optimal strategy in words including all steps and the final EMV. A B C D E F H 1 K L M N 0 P Q R s T U 1 2 NI is Non-Informer Inf is Informer P(Inf) = PINI) = Lie Detector 1 Pl+ | Inf) = PC- Inf) = 3 Savings: Fire and he is Informer $8,200,000 4 Cost: Fire and he is NOT Informer $13,000,000 5 Cost: Do Not Fire VP -$5,400,000 6 Cost Lie Detector 1 1 $285,000 7 Cost Lie Detector 2 $975,000 8 9 The "yellow" cells have probabilities and 10 the "blue" cells have node values. 11 You can use this prune in your tree: 12 The best strategy is to 13 14 Pl+ NI) = PC- INI) = Bayes: P(+) = P(+ | Inf) * P(Inf) + P(+NI) * P(NI) = P(Inf | +) = P(+ | Inf) * P(Inf) /P(+) = 15 PINI |-) = P(- | NI) * P(NI)/P(-) = Is Informer 16 17 18 19 20 21 22 23 $7,915,000 Fire VP A B C D E F H 1 1 J K L M N o P R S s T U V w Y Z Q Is Informer $7,915,000 Fire VP Is Not Informer Positive Result (Lying) Do Not Fire VP Use Lie Detector 1 o Is Informer Fire VP 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Is Not Informer Negative Result (Not Lying) Do Not Fire VP -$5,685,000 Is Informer Fire VP Is Not Informer Positive Result (Lying) 57 58 59 60 Do Not Fire VP A B D E F H K L M N O P Q R S T U 1 J Positive Result (Lying) Do Not Fire VP 55 56 57 58 58 59 60 4 61 62 63 64 65 66 67 68 69 Use "Perfect" Lie Detector 2 Is Informer Fire VP Is Not Informer Negative Result (Not Lying) Do Not Fire VP Is Informer Fire VP 70 71 72 73 74 75 76 77 78 79 80 31 82 83 84 85 36 87 88 89 90 91 92 92 93 94 95 Is Not Informer No Lie Detector $13,000,000 Do Not Fire VP