Decision Making without State Probabilities

1. Decision Making without State Probabilities This is called DMUU—Decision Making Under Uncertainty

2. Decision Criteria • no state probabilities??--Your model is one of UNCERTAINTY • use UNCERTAINTY criteria • got state probabilities??--Your model is one of RISK • use RISK criteria • (probabilities—probability information)

4. UNCERTAINTY Criteria—used when we don’t know the state probabilities • Based on DM’s attitude toward the risk • Pessimist, also called maximin • Optimist, also called maximax • in-betweenist • Insufficient reason • Regrettist, also called minimax regret

5. RISK Criteria • Based on expected or probabilistic considerations • Expected payoff or value • Expected Regret

6. Other RISK-related measures • Expected payoff of perfect information • Expected value of perfect information • Expected payoff of sample (imperfect) information • Expected value of sample [imperfect) information

7. Scenario • Consider the needs of a program manager who must decide which among several projects to bid on. • Due to resource constraints only one of the projects can be bid on • There are two future states—WIN the bid or LOSE the bid

8. The Payoff Table

9. Assume we don’t know the win/lose probabilities • So we have to use the UNCERTAINTY criteria • Pessimist criterion • Optimist criterion • Regrettist criterion • In-betweenist criterion • Insufficient reason criterion

10. PESSIMIST CRITERION 1) For each row, find the smallest payoff in the row and record that in a column to the right, labeled ROW MINIMUM 2) Examine the column to the right labeled ROW MINIMUM and pick the alternative with the largest payoff in that column.

11. Pessimist Criterion--best of all of the worst-case scenarios • Winner is… Do Nothing

12. OPTIMIST CRITERION 1) For each row, find the largest payoff in the row and record that in a column to the right, labeled ROW MAXIMUM 2) Examine the column to the right labeled ROW MAXIMUM and pick the alternative with the largest payoff in that column.

13. Optimist Criterion--best of all of the best-case scenarios • Winner is… Bid Project 2

14. IN-BETWEENIST CRITERION 1) For each row, combine the smallest payoff in the row with the largest payoff in the row using the formula: *ROW MIN + (1 - )*ROW MAX record that in a column to the right, labeled COMBINED; 2) Examine the column labeled COMBINED to the right and pick the alternative with the largest payoff in that column.

15. In-Betweenist Criterion—alpha= .5 • Winner is… Bid Project 2

16. REGRETTIST CRITERION 1) Form the regret table. 1) For each row in the regret table, find the largest regret number in the row and record that in a column to the right labeled ROW MAXIMUM. 2) Examine the column labeled ROW MAXIMUM to the right and pick the alternative with the smallest regret in that column.

17. Regret Criterion

18. Regret Table The Winner is… Bid Project 2

19. Two Environments • Decision-making under uncertainty • When we don’t know the state probabilities • Optimist, pessimist, in-betweenist, insufficient reason, regrettist • Decision-making under risk • When we do know the state probabilities • Expected value or payoff • Expected regret

20. Decision Making under Risk • Criteria • Expected value or payoff • Expected regret • Measures • Expected payoff of perfect information • Expected value of perfect information • Expected payoff of sample information • Expected value of sample information

21. DMUR Criterion DMUR (Decision-Making Under risk) Expected Value Criterion 1) For each row,calculate the product of the column probability with the payoff in that column and add up all of the products, recording the result in the column labeled EXPECTED VALUE to the right of the payoff table 2) Examine the column labeled EXPECTED VALUE to the right and pick the alternative with the largest payoff in that column.

22. DMUR--Expected Value Do Project 2!

23. EXPECTED REGRET Criterion 1) Form the regret table 2) For each row calculated its expected regret by taking the product of each state probability with the regret number in that column, summing all such products 3) Pick the alternative (i.e., row) whose expected regret is smallest This will always be the same alternative that gets chosen by the expected value or payoff criterion

24. Expected Regret Do Project 2 The Winner is…

25. Expected Value & Regret

26. Notes • For any alternative, the expected value and expected regret numbers sum to the expected payoff of perfect information • The expected value and expected regret criteria always select the same alternative, because when the former is maximized, the latter is minimized

27. Expected Payoff of Perfect Information, EPPI Calculated by finding the largest payoff in each column and then taking the products with the column probabilities and summing these products The EPPI is the best we could do if we had perfect information $70,000 for this problem

28. Expected Value of Perfect Information, EVPI by definition, EVPI = EPPI - EV* EVPI = $70,000 - $67,000 = $3,000 The EVPI is the value to us of the additional information The value is the “best we could do with the additional information” minus the “best we could do without the additional information”

29. More Notes • The minimum expected regret is also the EXPECTED VALUE OF PERFECT INFORMATION—THE ABSOLUTE MAXIMUM WE WOULD BE WILLING TO PAY FOR ADDITIONAL INFORMATION • PROOF??

33. RULE OF INSUFFICIENT REASON 1) For each row, add-up all of the payoffs in that row and record the result in a column to the right labeled ROW SUM. 2) Examine the column labeled ROW SUM to the right and pick the alternative with the largest payoff in that column.

34. Insufficient Reason • Winner is… Bid Project 2