1. Making Decisions Under Uncertainty
Decision Models
Making Decisions
Under Uncertainty

2. Decision Analysis Models
Decision Analysis is about making optimal decisions when the future is unknown.
A decision analysis model consists of:
A set of possible decisions
Discrete or continuous
Finite or infinite
A set of states of nature for the future
A “payoff” for each decision-state of nature combination
A return when a particular state of nature occurs after making a particular decision
For discrete, finite models – these can be summarized in a payoff table.

3. Example -- Tom Brown Investment
Tom Brown has $1000 to invest in:
Gold -- generally moves opposite of market
Bond -- generally moves with the market
Stock -- generally moves with the market
C/D -- pays same small amount regardless of market
Option -- generally moves with the market
How do we measure the market?
How do we determine payoffs?

4. Measuring the Market Could use DOW, NASDAQ, S&P, other, etc.
Let’s use the Dow
Could list every possible outcome for the DOW between 500 and 50,000 say
Here we define:
S1 -- Large Rise
(> 1500 point gain from current value)
S2 -- Small Rise
( point gain)
S3 -- No change
(decrease or increase of < 500 points)
S4 -- Small Fall
( point drop)
S5 -- Large Fall
(> 1200 point drop from current value)

5. The Payoff Table Which decision should be made?
Using the “rules of thumb”, the following are the estimates of the gains on a $1000 invetment
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
D5: Option
$500
Which decision should be made?

6. Dominated Strategies
Before deciding which decision should be made, we can eliminate one that will never be made.
We see that sometimes Gold is better than Bond and vice versa, Stock is better than CD and vice versa, etc.
But let’s look at the option vs. the bond
-$150
-$100
$150
$200
$250 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D2: Bond
D5: Option
-$200
The bond is always at least as good as the option! The option is dominated by the bond decision! Eliminate the option!

7. The Resulting Payoff Table
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
No decision alternative dominates any other decision alternative!

8. Decision Making Under Certainty
We are never “certain” about the future, but suppose we were.
Strategy: For the certain state of nature, choose the decision with the highest payoff
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
D1-Gold $200
D1-Gold $300
D3-Stock $500
D3-Stock $250
D4-C/D $60
For this certain
state of nature

9. Decision Making Under Uncertainty
Situation: We have no idea which state of nature will occur
Approach: Depends on the attitude of the decision maker
Optimistic
Pessimistic (Conservative)
Regrets Not Making Best Choice
Each state of Nature Equally Likely

10. Optimistic Decision Maker MAXIMAX Criterion
Optimist: No matter what decision I make, the best state of nature for that decision will occur
Max Payoff
List Maximum payoff for each decision
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
$300
$250
Highest -- Choose D3 - Stock
$500
$60

11. Pessimistic Decision Maker MAXIMIN Criterion
Pessimist: No matter what decision I make, the worst state of nature for that decision will occur
Min Payoff
List Minimum payoff for each decision
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
-$100
-$150
-$600
Highest -- Choose D4 - C/D
$60

12. “I Should Have” Decision Maker MINIMAX REGRET Criterion
The regret for a decision given a particular state of nature is the difference between the best payoff for that state of nature and the payoff for that decision given that state of nature

13. Payoff Table Regret Table -$100 -$150 $150 $200 $250 $60 -$200 -$600
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
Regret Table S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$600
$150 $0 $0
60 - 0
$60
$250
$50
$50
$400
$210 $0 $0
$100
$500
$660
500-60
$440
$190
250-60
200-60
$140
$240
300-60 $0

14. Pessimistic Regret Decision Maker MINIMAX REGRET Criterion
Pessimist: No matter what decision I make, the worst regret for that decision will occur
Max Regret
List Maximum regret for each decision
$600
$210
$400
$50
$250
$190
$500
$660
$150 $0
$60 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$440
$240
$140
$100
Regret Table
$600
$400
Lowest -- Choose D2 - Bond
$660
$440

15. Indifferent Decision Maker INSUFFICIENT REASON Criterion
Indifference: Each state of nature is equally likely
Average Value: Best is one with highest average
Average
Payoffs
List Sum of payoffs for each decision
-$100
-$150
$150
$200
$250
$60
-$200
-$600
$100
$300 $0 S1
Lg Rise S2
Sm Rise S3
No Chg. S4
Sm Fall S5
Lg Fall
D1: Gold
D2: Bond
D3: Stock
D4: C/D
$500
$100
Highest -- Choose D1 - Gold
$70
$10
$60

16. Using the Decision Template
Enter Decision Names, State Names, Payoffs
Optimal

17. Summary of Decisions Depends on the approach of the decision maker!
Optimistic Stock
Pessimistic C/D
Pessimistic Regret Bond
Indifference Gold
Which one should be chosen?
Depends on the approach of the decision maker!

18. Review Decision Models Dominated Strategies
Decisions, States Of Nature, Payoffs
Dominated Strategies
Decision Making Under Certainty
Decision Making Under Uncertainty
Optimistic Maximax
Pessimistic Maximin
Pessimistic Regret Minimax Regret
Indifference Insufficient Reason
Use of Decision Template