1. Decision Analysis

2. Basic Terms Decision Alternatives (eg. Production quantities)
States of Nature (eg. Condition of economy)
Payoffs ($ outcome of a choice assuming a state of nature)
Criteria (eg. Expected Value)

3. What kinds of problems? Alternatives known
States of Nature and their probabilities are known.
Payoffs computable under different possible scenarios

4. Decision Environments
Ignorance – Probabilities of the states of nature are unknown, hence assumed equal Risk / Uncertainty – Probabilities of states of nature are known Certainty – It is known with certainty which state of nature will occur. Trivial problem.

5. Example – Decisions under Ignorance
Assume the following payoffs in $ thousand for 3 alternatives – building 10, 20, or 40 condos. The payoffs depend on how many are sold, which depends on the economy. Three scenarios are considered - a Poor, Average, or Good economy at the time the condos are completed.
Payoff Table S1
(Poor) S2
(Avg) S3
(Good)
A1 (10 units)
300
350
400
A2 (20 units)
-100
600
700
A3 (40 units)
-1000
-200
1200

6. Maximax - Risk Seeking Behavior
What would a risk seeker decide to do? Maximize payoff without regard for risk. In other words, use the MAXIMAX criterion. Find maximum payoff for each alternative, then the maximum of those. S1 S2 S3
MAXIMAX A1
300
350
400 A2
-100
600
700 A3
-1000
-200
1200
The best alternative under this criterion is A3, with a potential payoff of 1200.

7. Maximin – Risk Averse Behavior
What would a risk averse person decide to do? Make the best of the worst case scenarios. In other words, use the MAXIMIN criterion. Find minimum payoff for each alternative, then the maximum of those. S1 S2 S3
MAXIMIN A1
300
350
400 A2
-100
600
700 A3
-1000
-200
1200
The best alternative under this criterion is A1, with a worst case scenario of 300, which is better than other worst cases.

8. LaPlace – the Average
What would a person somewhere in the middle of the two extremes choose to do? Take an average of the possible payoffs. In other words, use the LaPlace criterion (named after mathematician Pierre LaPlace). Find the average payoff for each alternative, then the maximum of those. S1 S2 S3
LaPlace A1
300
350
400 A2
-100
600
700 A3
-1000
-200
1200
The best alternative under this criterion is A2, with an average payoff of 400, which is better than the other two averages.

9. Example – Decisions under Risk
Assume now that the probabilities of the states of nature are known, as shown below. S1
(Poor) S2
(Avg) S3
(Good)
A1 (10 units)
300
350
400
A2 (20 units)
-100
600
700
A3 (40 units)
-1000
-200
1200
Probabilities
0.30
0.60
0.10

10. Expected Values
When probabilities are known, compute a weighed average of payoffs, called the Expected Value, for each alternative and choose the maximum value.
Payoff Table S1 S2 S3 EV A1
300
350
400
340 A2
-100
600
700 A3
-1000
-200
1200
-300
Probabilities
0.30
0.60
0.10
The best alternative under this criterion is A2, with a maximum EV of 400, which is better than the other two EVs.

11. Expected Opportunity Loss (EOL)
Compute the weighted average of the opportunity losses for each alternative to yield the EOL.
Opportunity Loss (Regret) Table S1 S2 S3
EOL A1
250
800
230 A2
400
500
170 A3
1300
870
Probabilities
0.30
0.60
0.10
The best alternative under this criterion is A2, with a minimum EOL of 170, which is better than the other two EOLs.
Note that EV + EOL is constant for each alternative! Why?

12. EVUPI: EV with Perfect Information
If you knew everytime with certainty which state of nature was going to occur, you would choose the best alternative for each state of nature every time. Thus the EV would be the weighted average of the best value for each state. Take the best times the probability, and add them all.
300*0.3 = 90
600*0.6 = 360
1200*0.1 = 120
_____________
Sum =
Thus EVUPI = 570 S1
(Poor) S2
(Avg) S3
(Good)
A1 (10 units)
300
350
400
A2 (20 units)
-100
600
700
A3 (40 units)
-1000
-200
1200
Probabilities
0.30
0.60
0.10

13. EVPI: Value of Perfect Information
If someone offered you perfect information about which state of nature was going to occur, how much is that information worth to you in this decision context?
Since EVUPI is 570, and you could have made 400 in the long run (best EV without perfect information), the value of this additional information is = 170.
Thus, EVPI = EVUPI – Evmax
= EOLmin

14. Decision Tree
| 300
0.3
340
0.6
| 350
0.1
| 400 A1
| -100
0.3 A2
0.6
| 600 A2
400
400
0.1
| 700 A3
0.3
| -1000
0.6
| -200
-300
0.1
| 1200