CD9s-1
CD Supplement to Chapter 9 Decision Criteria
Review Questions
9s-1 It might be desirable to use a decision criterion that doesn’t rely on the prior probabilities
if these probabilities are not reliable.
9s-2 The maximax criterion is a very optimistic criterion that focuses on the best that can
happen by choosing the alternative that can yield the maximum of the maximum payoffs.
9s-4 The pessimism-optimism index measures where the decision-maker falls on a scale from
totally pessimistic to totally optimistic. This index is used with the realism criterion to
9s-6 The regret from having chosen a particular decision alternative is the maximum payoff
minus the actual payoff.
9s-7 The regret that can be felt afterward if the decision does not turn out well is being
minimized with the minimax regret criterion.
9s-8 A totally optimistic person would find the maximax criterion appealing, while a totally
pessimistic person would find the maximin criterion appealing. The realism criterion
9s-9 There is no uniformly reasonable criterion that doesn’t use prior probabilities.
9s-10 The maximum likelihood criterion focuses on the most likely state of nature.
9s-11 The main criticism of the maximum likelihood criterion is that it does not consider the
CD Supplement to Chapter 9 – Decision Criteria
CD9s-3
d) Choose A3 to minimize the maximum regret ($3,000).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative S1 S2
A1 1 7
A2 6 3
A3 4 4
Maximum 6 7 0 0 0
Regret Table
State of Nature Maximum
Alternative S1 S2 in Row
A1 5 0 5
A2 0 4 4
A3 2 3 3 Minimax
9s.2 a) A3 should be chosen for a maximax payoff of 35.
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A B C D E F G H I
Template for Maximax Criterion
State of Nature Maximum
Alternative S1 S2 S3 in Row
A1 15 30 20 30
A2 12 24 28 28
A3 525 35 35 Maximax
A4 18 20 25 25
b) A4 should be chosen with a maximin payoff of 18.
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A B C D E F G H I
Template for Maximin Criterion
State of Nature Minimum
Alternative S1 S2 S3 in Row
A1 15 30 20 15
A2 12 24 28 12
A3 525 35 5
A4 18 20 25 18 Maximin
CD9s-4
c)
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A B C D E F G H I J K
Template for Realism Criterion
Pessimism-Optimism Index = 0.5
State of Nature Maximum Minimum Weighted
Alternative S1 S2 S3 in Row in Row Payoff
A1 15 30 20 30 15 22.5 Maximum
A2 12 24 28 28 12 20
A3 525 35 35 520
A4 18 20 25 25 18 21.5
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A B C D E F G H I J K
Pessimism–Optimism Index = 0.25
State of Nature Maximum Minimum Weighted
Alternative S1 S2 S3 in Row in Row Payoff
A1 15 30 20 30 15 18.75
A2 12 24 28 28 12 16
A3 525 35 35 5 12.5
A4 18 20 25 25 18 19.75 Maximum
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A B C D E F G H I J K
Pessimism–Optimism Index = 0.75
State of Nature Maximum Minimum Weighted
Alternative S1 S2 S3 in Row in Row Payoff
A1 15 30 20 30 15 26.25
A2 12 24 28 28 12 24
A3 525 35 35 5 27.5 Maximum
A4 18 20 25 25 18 23.25
d) Choose A2 to minimize the maximum regret (7).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative S1 S2 S3
A1 15 30 20
A2 12 24 28
A3 525 35
A3 18 20 25
Maximum 18 30 35 0 0
Regret Table
State of Nature Maximum
Alternative S1 S2 S3 in Row
A1 3 0 15 15
A2 6 6 7 7 Minimax
A3 13 5 0 13
A3 010 10 10
9s.3 a) Build computers (maximax profit is $54 million).
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A B C D E F G H I
Template for Maximax Criterion
State of Nature Maximum
Alternative Sell 10,000 Sell 100,000 in Row
Build Computers 0 54 54 Maximax
Sell Rights 15 15 15
b) Sell the rights (maximin profit is $15 million).
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A B C D E F G H I
Template for Maximin Criterion
State of Nature Minimum
Alternative Sell 10,000 Sell 100,000 in Row
Build Computers 0 54 0
Sell Rights 15 15 15 Maximin
c) Build computers (weighted payoff = $27 million).
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A B C D E F G H I J K
Template for Realism Criterion
Pessimism-Optimism Index = 0.5
State of Nature Maximum Minimum Weighted
Alternative Sell 10,000 Sell 100,000 in Row in Row Payoff
Build Computers 0 54 54 027 Maximum
Sell Rights 15 15 15 15 15
d) Build computers (minimax regret of $15 million).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative Sell 10,000 Sell 100,000
Build Computers 0 54
Sell Rights 15 15
Maximum 15 54 0 0 0
Regret Table
State of Nature Maximum
Alternative Sell 10,000 Sell 100,000 in Row
Build Computers 15 015 Minimax
Sell Rights 0 39 39
9s.4 a) Buy 13 cases (maximax profit of $65).
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A B C D E F G H I
Template for Maximax Criterion
State of Nature Maximum
Alternative Sell 10 Sell 11 Sell 12 Sell 13 in Row
Buy 10 $50 $50 $50 $50 $50
Buy 11 $47 $55 $55 $55 $55
Buy 12 $44 $52 $60 $60 $60
Buy 13 $41 $49 $57 $65 $65 Maximax
CD9s-6
b) Buy 10 cases (maximin profit of $50).
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A B C D E F G H I
Template for Maximin Criterion
State of Nature Minimum
Alternative Sell 10 Sell 11 Sell 12 Sell 13 in Row
Buy 10 $50 $50 $50 $50 $50 Maximin
Buy 11 $47 $55 $55 $55 $47
Buy 12 $44 $52 $60 $60 $44
Buy 13 $41 $49 $57 $65 $41
c) Buy 13 cases (maximum weighted profit of $53).
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A B C D E F G H I J K
Template for Realism Criterion
Pessimism-Optimism Index = 0.5
State of Nature Maximum Minimum Weighted
Alternative Sell 10 Sell 11 Sell 12 Sell 13 in Row in Row Payoff
Buy 10 $50 $50 $50 $50 $50 $50 $50
Buy 11 $47 $55 $55 $55 $55 $47 $51
Buy 12 $44 $52 $60 $60 $60 $44 $52
Buy 13 $41 $49 $57 $65 $65 $41 $53 Maximum
CD9s-7
d) Buy 12 cases (minimax regret of $6).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative Sell 10 Sell 11 Sell 12 Sell 13
Buy 10 $50 $50 $50 $50
Buy 11 $47 $55 $55 $55
Buy 12 $44 $52 $60 $60
Buy 13 $41 $49 $57 $65
Maximum $50 $55 $60 $65 $0
Regret Table
State of Nature Maximum
Alternative Sell 10 Sell 11 Sell 12 Sell 13 in Row
Buy 10 $0 $5 $10 $15 $15
Buy 11 $3 $0 $5 $10 $10
Buy 12 $6 $3 $0 $5 $6 Minimax
Buy 13 $9 $6 $3 $0 $9
CD9s-8
e) Buy 11 cases (maximum profit of $55).
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A B C D E F G H
Template for Maximum Likelihood Criterion
State of Nature
Alternative Sell 10 Sell 11 Sell 12 Sell 13
Buy 10 $50 $50 $50 $50
Buy 11 $47 $55 $55 $55 Maximum
Buy 12 $44 $52 $60 $60
Buy 13 $41 $49 $57 $65
Prior Probability 0.2 0.4 0.3 0.1
Maximum
f) Buy 12 cases (maximum average profit of $54).
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A B C D E F G H I
Template for Equally Likely Criterion
State of Nature Row
Alternative Sell 10 Sell 11 Sell 12 Sell 13 Average
Buy 10 $50 $50 $50 $50 $50
Buy 11 $47 $55 $55 $55 $53
Buy 12 $44 $52 $60 $60 $54 Maximum
Buy 13 $41 $49 $57 $65 $53
9s.5 a) Choose A1 (minimax regret = 3).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative S1 S2
A1 12 17
A2 13 15
A3 15 12
A4 020
Maximum 15 20 0 0 0
Regret Table
State of Nature Maximum
Alternative S1 S2 in Row
A1 3 3 3 Minimax
A2 2 5 5
A3 0 8 8
A4 15 015
CD9s-9
b) Choose A2 (minimax regret = 2).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative S1 S2
A1 12 17
A2 13 15
A3 15 12
Maximum 15 17 0 0 0
Regret Table
State of Nature Maximum
Alternative S1 S2 in Row
A1 3 0 3
A2 2 2 2 Minimax
A3 0 5 5
c) The above answers demonstrate the objection that making choices between serious
alternatives can depend on irrelevant alternatives with this criterion.
9s.6 a) Choose the speculative investment (maximax payoff of $40 million).
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A B C D E F G H I
Template for Maximax Criterion
State of Nature Maximum
Alternative Improving Stable Worsening in Row
Conservative 30 5 –10 30
Speculative 40 10 –30 40 Maximax
Counter-cyclical -10 0 15 15
b) Choose either the conservative or the counter-cyclical investment
(maximin payoff = –$10 million).
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A B C D E F G H I
Template for Maximin Criterion
State of Nature Minimum
Alternative Improving Stable Worsening in Row
Conservative 30 5 –10 -10 Maximin
Speculative 40 10 -30 -30
Counter-cyclical -10 0 15 –10 Maximin
c) Choose the conservative investment (maximum weighted payoff of $10 million).
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A B C D E F G H I J K
Template for Realism Criterion
Pessimism-Optimism Index = 0.5
State of Nature Maximum Minimum Weighted
Alternative Improving Stable Worsening in Row in Row Payoff
Conservative 30 5 -10 30 -10 10 Maximum
Speculative 40 10 -30 40 -30 5
Counter-cyclical
-10 0 15 15 –10 2.5
CD9s-10
d) Choose the conservative investment (minimax regret of $25 million).
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A B C D E F G H I
Template for Minimax Regret Criterion
Payoff Table
State of Nature
Alternative Improving Stable Worsening
Conservative 30 5 –10
Speculative 40 10 -30
Counter-cyclical –10 0 15
Maximum 40 10 15 0 0
Regret Table
State of Nature Maximum
Alternative Improving Stable Worsening in Row
Conservative 10 525 25 Minimax
Speculative 0 0 45 45
e) Choose the speculative investment (maximum payoff when stable economy = $10
million).
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A B C D E F G H
Template for Maximum Likelihood Criterion
State of Nature
Alternative Improving Stable Worsening
Conservative 30 5 -10
Speculative 40 10 -30 Maximum
Counter-cyclical -10 0 15
Prior Probability 0.1 0.5 0.4
Maximum
f) Choose the conservative investment (maximum average payoff is $8.33 million).
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A B C D E F G H I
Template for Equally Likely Criterion
State of Nature Row
Alternative Improving Stable Worsening Average
Conservative 30 5 -10 8.33 Maximum
Speculative 40 10 -30 6.67
Counter-cyclical -10 0 15 1.67