Incorporating New Information - University of Washington

Session #8 The Value of Information, Risk Aversion, and Utilities

Incorporating New Information

Page 1

Often, a preliminary study can be done to better determine the true state of nature.

Examples: ? Market surveys

? Test-marketing

? Seismic testing (for oil)

Question: What is the value of this information?

Session #8 The Value of Information, Risk Aversion, and Utilities

Page 2

Expected Value of Perfect Information (EVPI)

Consider again the problem faced by an oil company that is trying to decide whether to drill an exploratory oil well on a given site. Drilling costs $200,000. If oil is found, it is worth $800,000. If the well is dry, it is worth nothing. The prior probability that the site is wet is estimated at 40%.

Payoff Table and Probabilities:

Decision Drill

Do not drill Prior Probability

State of Nature

Wet

Dry

600

-200

0

0

0.4

0.6

All payoffs are in thousands of dollars

Suppose there was a test that could predict whether the site was wet or dry. Expected Payoff =

Value of Perfect Information =

A

BC

D

E

FG

H

I

J

K

1

2

Drill

3

0.4

600

4

Wet

600

600

5

1

6

0

600

7

Do not drill

8

0

9

0

0

10

11

240

12

Drill

13

0.6

-200

14

Dry

-200

-200

15

2

16

0

0

17

Do not drill

18

0

19

0

0

Session #8 The Value of Information, Risk Aversion, and Utilities

Imperfect Information (Seismic Test)

Page 3

Suppose a seismic test is available that would better indicate whether or not the site was wet or dry.

Record of 100 Past Seismic Test Sites

Seismic Result

Good (G) Bad (B)

Total

Actual State of Nature

Wet (W) Dry (D)

30

20

10

40

40

60

Total

50 50 100

A BC

D

E

1

2

3

4

5

6

7

P(G) = ?

8

Good Test (G)

9

10

11

12

13

14

15

16

17

18

19

P(B) = ?

20

Bad Test (B)

21

22

23

24

FG H Drill

I JK

L

M

P(W | G) = ?

Wet

P(D | G) = ? Dry

Do not drill

Drill

P(W | B) = ? Wet

P(D | B) = ? Dry

Do not drill

NO 600

-200 0

600

-200 0

Conditional Probability: P(W|G) = probability site is "Wet" given that it tested "Good"

Session #8 The Value of Information, Risk Aversion, and Utilities

Conditional Probabilities

Page 4

Seismic Result

Good (G) Bad (B)

Total

Actual State of Nature

Wet (W) Dry (D)

30

20

10

40

40

60

Total

50 50

100

Need probabilities of each test result: P(G) = P(B) =

Need conditional probabilities of each state of nature, given a test result: P(W | G) = P(D | G) = P(W | B) = P(D | B) =

How does the test help? Before Test

After Test

P(W) = 0.4

Session #8 The Value of Information, Risk Aversion, and Utilities

Page 5

Expected Value of Sample Information (EVSI)

A BC

D

E

FG

H

I

JK

L

M NO

P

QR S

1

0.6

2

Wet

3

600

4

Drill

800

600

5

6

-200

280

0.4

7

0.5

Dry

8

Good Test (G)

-200

9

1

0 -200

10

0

280

11

12

Do not drill

13

0

14

0

0

15

Do Seismic Test

16

0.2

17

0

140

Wet

18

600

19

Drill

800

600

20

21

-200

-40

0.8

22

0.5

Dry

23

Bad Test (B)

-200

24

2

0 -200

25

0

0

26

27

1

Do not drill

28

140

0

29

0

0

30

31

0.4

32

Wet

33

600

34

Drill

800

600

35

36

-200

120

0.6

37

Dry

38

Forego test

-200

39

1

0 -200

40

0

120

41

42

Do not drill

43

0

44

0

0

Expected Value of Sample Information (EVSI) =

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