Decision Analysis

1
Chapter 14

• Decision Analysis Part 4

2
Agenda

• Bayes Theorem
• Utility Theory
• HW25 (if we have time)

3
Review

• Weve 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
Lobbying Results Lobbying Results
State of Nature Positive Negative
Favorable Vote, s1 P (P s1) .90 P (N s1) .10
Unfavorable Vote, s2 P (P s2) .25 P (N s2) .67
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Bayes Theorem - Positive
PRIOR P (Sj) CONDITIONAL Pos Sj JOINT P (Pos Ç Sj) POSTERIOR P (Sj Pos)
Fav 0.550 0.90
Unfav 0.450 0.25
1.000   1.000
9
Bayes Theorem - Negative
PRIOR P (Sj) CONDITIONAL Neg Sj JOINT P (Neg Ç Sj) POSTERIOR P (Sj Neg)
Fav 0.550 0.10
Unfav 0.450 0.75
1.000   1.000
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
B
20.046
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
C
57.5
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?

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Utility

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

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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)

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Utility Example

• Based on past experience, youve developed the
  following payoff table and likelihoods

Alts States of Nature States of Nature States of Nature
Alts Superior (s1) .3 Moderate (s2) .5 Poor (s3) .2
Print (d1) 15,000 10,000 -5,000
TV (d2) 50,000 15,000 -30,000
PR (d3) 0 0 0
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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

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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.

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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

• Lets 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
Monetary Value Indifference Value of p Utility Value
50000 N/A 10
15000 .90 9
10000 .80 8
0 .75 7.5
-5000 .65 6.5
-30000 N/A 0
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Payoff Table in Terms of Utility
Alts States of Nature States of Nature States of Nature
Alts Superior (s1) .3 Moderate (s2) .5 Poor (s3) .2
Print (d1) 9 8 6.5
TV (d2) 10 9 0
PR (d3) 7.5 7.5 7.5
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
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For Next Class

• Continue with homework assignments (well review
  some in class)
• Be prepared to work with your partner on Case 1