Chapter 14

1. Chapter 14 Decision Analysis – Part 4

2. Agenda • Bayes Theorem • Utility Theory • HW#25 (if we have time)

3. Review • We’ve been able to: • Create payoff table • Calculate EMV and EVPI given likelihoods • Can perform sensitivity analysis to determine ranges for decisionmaking • Can seek additional information to get a better assessment of likelihoods • Can compare EVSI to EVPI to determine the efficiency of obtaining additional information

4. Sample Information • Once we obtain sample information, we can identify conditional probabilities for each outcome of the survey • Example: Positive lobbying, Negative lobbying • With knowledge of conditional probabilities, we can use Bayes’ Theorem to compute branch probabilities (posterior probabilities)

5. Bayes’ Theorem - Terms • Prior Probabilities: Original likelihoods without sample information • Conditional Probabilities: Probability of a sample outcome given a state of nature • P (Positive Lobbying | Favorable Vote) • P (Positive Lobbying | Negative Vote) • P (Negative Lobbying | Favorable Vote) • P (Negative Lobbying | Negative Vote)

6. Bayes’ Theorem - Terms • Joint Probabilities: Each Prior Probability multiplied by the Corresponding Conditional Probability • Sum of Joint Probabilities: The probability of the sample condition • Posterior Probabilities: Each Joint Probability divided by the sum of the Joint Probability

7. Restaurant Example • Prior Probabilities: • Favorable Vote: .55 • Unfavorable Vote: .45 • Conditional Probabilities: NEW INFORMATION

8. Bayes Theorem - Positive

9. Bayes Theorem - Negative

10. Fav .82 NOTICE THE REVISED #S: 60 50 80 30 100 0 A Unfav .18 Positive .61 B Fav .82 Unfav .18 C Fav .82 Lobby Effort Unfav .18 Fav .14 60 50 80 30 100 0 A Unfav .86 B Fav .14 Unfav .86 Negative .39 C Fav .14 Unfav .86

11. Fav .55 60 50 80 30 100 0 A Unfav .45 B Fav .55 Unfav .45 No Lobby Effort C Fav .55 Unfav .45

12. 58.2 Fav .82 NOTICE THE REVISED #S: 60 50 80 30 100 0 A Unfav .18 71 Positive .61 B Fav .82 Unfav .18 50.02 82 70.066 C Fav .82 Lobby Effort Unfav .18 Fav .14 60 50 80 30 100 0 51.4 A Unfav .86 37 20.046 B Fav .14 Unfav .86 Negative .39 14 C Fav .14 Unfav .86

13. Fav .55 60 50 80 30 100 0 55.5 A Unfav .45 57.5 B Fav .55 Unfav .45 No Lobby Effort 55 57.5 C Fav .55 Unfav .45

14. Utility • Question: Will you always want to choose the alternative with the highest EMV? • What other factors might you consider when selecting an alternative? EXAMPLES?

15. Utility • Utility is a measure of the total worth of a particular outcome • It reflects the decision maker’s attitude toward a variety of factors such as profit, loss, risk

16. Utility Example • You are a Marketing Manager who must decide on an advertising strategy for a new product rollout. • You have 3 decision alternatives: • Print Campaign (d1) • TV Campaign (d2) • Public Relations Only (d3) • Monetary payoffs associated with the campaign decision depend on the product reviews that you receive in the press: • Superior (s1) • Moderate (s2) • Poor (s3)

17. Utility Example • Based on past experience, you’ve developed the following payoff table and likelihoods:

18. Utility Example • Using EMV approach, you can determine the optimal choice: EMV1 = 15000(.3) + 10000(.5) + -5000(.2) = EMV2 = 50000(.3) + 15000(.5) + -30000(.2) = EMV3 = 0(.3) + 0(.5) + 0(.2) = Choose:

19. Utility Example • What happens if you select TV and the reviews are poor? Are you comfortable with the possibility of a $30,000 loss? • If you were risk averse, you would likely choose Print. • If you were unwilling to take ANY risk, you would likely choose PR. • Can establish utility values for the payoffs and then select the alternative with the highest utility instead of the highest EMV.

20. Establishing Utility Values • Step 1: Assign a utility value to the best and worst payoffs (arbitrary– but best payoff has to have a higher utility than the worst). • Utility of -30,000 = U(-30000) = 0 • Utility of 50,000 = U(50000) = 10 • Step 2: Determine a utility value for every other payoff

21. Establishing Utility Values • Consider a utility value from your payoff table: 15,000. • Compare your preference for a guaranteed payoff of 15,000 vs. the following gamble: • Payoff of 50,000 with a probability p and a payoff of -30,000 with a probability of (1-p) • You, as the decision maker, select the value of p that makes you indifferent between choosing the 15,000 or the gamble.

22. Establishing Utility Values • If you are indifferent when p = .90, then: • U(15,000) = pU(50,000) + (1-p)U(-30,000) • U(15,000) = .90(10) + (.10)(0) = • U(15,000) = 9 • EV(Gamble) = .90(50000) + .10(-30000) = 45,000-3000 = 42,000 You would rather have $15,000 for certain than incur a 10% risk of losing $30,000.

23. Establishing Utility Values • Let’s calculate utililty value for -5,000, assuming you are indifferent when p = .65: • U(-5,000) = pU(50,000) + (1-p)U(-30,000) • U(-5,000) = .65(10) + (.35)(0) = • U(15,000) = 6.5 • EV(Gamble) = .65(50000) + .35(-30000) = 32,500-10,500 = 22,000 You would rather have $22,000 for certain than incur a 35% risk of losing $30,000.

24. Establishing Utility Values • Can use the following equation to compute the utility for a specific monetary value, M: U(M) = pU(50,000) + (1-p)U(-30,000) = p(10) + (1-p)0 = 10p

25. Establishing Utility Values

26. Payoff Table in Terms of Utility • EU1 = 9(.3) + 8(.5) + 6.5(.2) = 8.0 • EU2 = 10(.3) + 9(.5) + 0(.2) = 7.5 • EU3 = 7.5(.3) + 7.5(.5) + 7.5(.2) = 7.5 • Choose Alternative 1 – Print

27. For Next Class • Continue with homework assignments (we’ll review some in class) • Be prepared to work with your partner on Case #1