Problem_Session_6

# Problem_Session_6 - MS&amp;E 252 Problem Session 6 11/14/06...

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11/14/06 MS&E 252 Problem Session 6 1 MS&E 252 Decision Analysis I Problem Session 6

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11/14/06 MS&E 252 Problem Session 6 2 Announcements Midterm solutions are available online Case study: Don’t forget to meet with your section TA this week. Sign-up through coursework discussion. Homework 6 due this week, final homework assigned after Thanksgiving
11/14/06 MS&E 252 Problem Session 6 3 Exponential u-curves revisited Recall the equation for risk-averse and risk- seeking delta people In general, the coefficient ‘b’ can be any value other than 0 or 1 However, since the decision nodes are MAX functions, you must have a u-curve that increases in wealth or you won’t make the best choice. Thus: b should never equal 0 if r > 1 (risk averse), b should be < 0 if r < 1 (risk seeking), b should be > 0 x br a x u - + = ) (

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11/14/06 MS&E 252 Problem Session 6 4 What concepts do we expect you to master? Sensitivity Analysis Why is it important? Examples of Sensitivity Analysis Information Gathering Value of Information Rain Bets Case Study
11/14/06 MS&E 252 Problem Session 6 5 Sensitivity Analysis

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11/14/06 MS&E 252 Problem Session 6 6 What do we mean by sensitivity analysis? Why is it important? How does the best decision change as the probability of sun changes? How does the certain equivalent change as the probability of sun changes? How does the value of clairvoyance change as the probability of sun changes? “How does this change when you change that?” p 0 0.2 0.4 0.6 0.8 1 \$150 \$100 \$50 \$0
11/14/06 MS&E 252 Problem Session 6 7 Sensitivity analysis helps derive important insights about the decision situation. Using sensitivity analysis, we can tell how accurate our assessments need to be. p 0 0.2 0.4 0.6 0.8 1 \$150 \$100 \$50 \$0 “How does this change when you change that?” What do we mean by sensitivity analysis? Why is it important?

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11/14/06 MS&E 252 Problem Session 6 8 Eduardo, a confused graduate student, has just won the MS&E weekly Bingo prize in which he has his choice among three alternatives. Here is an example of what Sensitivity Analysis allows you to do… Although he follows the five rules of actional thought, he can't decide which alternative to pick and has asked for your help.
11/14/06 MS&E 252 Problem Session 6 9 In the first alternative, he is given a jar of balls, some are red and the others are white. If Eduardo picks a red ball, he wins \$750, if he picks a white ball, he wins \$400. The second alternative is a similar deal. However if he picks a red ball from the jar, he wins \$1000, if not, he wins nothing. The third alternative is a sure \$500. Assume he is risk neutral. Here is an example of what Sensitivity Analysis allows you to do…

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11/14/06 MS&E 252 Problem Session 6 10 Value of Clairvoyanc e?
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## This note was uploaded on 06/16/2010 for the course MS&E 252 taught by Professor Howard during the Fall '08 term at Stanford.

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Problem_Session_6 - MS&amp;E 252 Problem Session 6 11/14/06...

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