In the fourth Austin Powers movie Austin Powers: Decisions Are Forever the film opens with the notorious Dr. Evil is trying to decide how to extort thousands out of the worlds major powers. He has three plans: D1: Take control of the worlds radio stations and play nothing but N Sync, Back Street Boys and Britney Spears to mask his subliminal PAY ME messages. D2: Seize all the television relay satellites and broadcast only Chum/City shows like Fashion TV, MusicTV, TVTV, MyTV, YourTV, EvilTV, etc, turning the mass viewing audiences minds to mush. D3: Hypnotizing Oprah so that she puts Dr. Evils My Plan for World Domination on Oprahs Book List. The success of these plans depends on how bright Austin Powers assistant proves to be: S1: Ilene Dover normally competent, but too prone to falling off high places. S2: Sharon Secrets clever, but too prone to thinking out loud. S3: Karen Hope thorough, but too concerned about whether the other guy the enemy, and bad guy gets hurt. Number Two has analyzed the potential payoffs of the three plans in each state: Dr. Evil has called a meeting of his Supreme Council his son, Scott; his miniscule alter ego, Mini-Me; his new love, Lacy Laplace; and his trusted Number Two for advice. My fine young son, Scott, what do you think we should do? You guys are all so incompetent! Its embarrassing having you for a father! The kids at school ridicule me: You fathers the most inept bad guy in the world. Im very pessimistic about what you can do. Id play it conservative. Very well. When I want your advice, Ill ask for it. You just did, you moron! shot back Scott. Never mind. What about you, Lacy? It is obvious that I would use the Laplace criteria, she purred. And Mini-Me? Mini-Me gestures a big sweeping upward motion. Yes, of course, you are so wonderfully aggressive. You want us to go for the big win. I like that in us! But with all due respect, Dr. Evil, I think we should look at what might go wrong. I hate to look back and think we made the wrong decision. We should analyze how much we lose by making the wrong choice, counseled Number Two. Required:

(a) What criteria are suggested by each of Dr. Evils advisors, and which decision would each suggest? Support your answers with the appropriate supporting analysis. (Note: The Laplace criteria determines the decision by either summing the payoffs for the decision or equivalently by assigning equal weights to each outcome and computing the expected value.)

(b) Suppose that Dr. Evil has determined that the probability of Austin Powers assistants are P(S1 Ilene Dover) = 0.25; P(S2 Sharon Secrets) = 0.45; and P(S3 Karen Hope) = 0.30. i. What would be the optimal decision for the risk neutral decision maker? ii. How much would Dr. Evil pay to know with absolute certainty which of the assistants Austin Powers would be working with? What do we call this value? Support your answers with the appropriate supporting analysis.

(c) Subsequent to this analysis, Dr. Evil gets a report back from his spy, Floyd Flewellyn who knows that the choice of agent will depend on which Director of MI96, the counterspy agency, is in charge of the Dr. Evil file. When Ilene Dover has been assigned to a mission, she was appointed by Rowen Ramsbottom 84% of the time and Seymour Shuttlecock 16% of the time. Basil Bottomley has never assigned Ilene Dover to a mission. When Sharon Secrets has been assigned to a mission, she was appointed by Seymour Shuttlecock 80% of the time and Basil Bottomley 20% of the time. Rowen Ramsbottom has never assigned Sharon Secrets to a mission. When Karen Hope has been assigned to a mission, she was appointed by Rowen Ramsbottom 30% of the time and Basil Bottomley 70% of the time. Seymour Shuttlecock has never assigned Karen Hope to a mission. How much would Dr. Evil be willing to pay Floyd Flewellyn to know exactly which Director would be in charge of the Dr. Evil file?

(d) Construct a complete tree diagram of Dr. Evils decision problem.