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 90% certain that this informer is the vice president of finance, whose contacts have been extremely valuable in obtaining financing for the company. If she decides to fire this vice president and he is the informer, she estimates that the company will gain $500,000. If she decides to fire this vice president but he is not the informer, the company will lose his expertise and still have an informer within the staff; the CEO estimates that this outcome would cost her company about $2.5 million. If she decides not to fire this vice president, she estimates that the firm will lose $1.5 million regardless of whether he actually is the informer (because in either case the informer is still with the company). Before deciding whether to fire the vice president for finance, the CEO could order 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 $150,000.
Another problem she must consider is that the available lie detector tests are not perfectly reliable. In particular, if a person is lying, the test will reveal that the person is lying 95% of the time. Furthermore, if a person is not lying, the test will indicate that the person is not lying 85% of the time.
a. To minimize the expected total cost of managing this difficult situation, what strategy should the CEO adopt?
b. Should the CEO order the lie detector tests for all of her employees? Explain why or why not.
c. Determine the maximum amount of money that the CEO should be willing to pay to administer lie detector tests.
d. How sensitive are the results to the accuracy of the lie detector test? Are there any “reasonable” values of the error probabilities that change the optimal strategy?