456552326-Decision-1-Decision-tree-2019-ppt.ppt
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Oct 27, 2025
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About This Presentation
A Decision Tree is presented here as an inductive learning task, meaning it learns from specific examples or data to make generalized conclusions. In other words, it observes patterns from known cases (facts) and uses them to predict outcomes for new, unseen situations.
Slide Content
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Decision Analysis: Decision Analysis:
Decision TreeDecision Tree
Prof. U.K. Prof. U.K.
BhattacharyaBhattacharya
Decision Analysis: Decision Analysis:
Decision TreeDecision Tree
Prof. U.K. Prof. U.K.
BhattacharyaBhattacharya
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Introduction to Decision AnalysisIntroduction to Decision Analysis
•The field of decision analysis provides a framework for
making important decisions.
•Decision analysis allows us to select a decision from a set of
possible decision alternatives when uncertainties regarding
the future exist.
The goal is to optimize the resulting payoff in terms of a
decision criterion.
Example
Introduction to Decision AnalysisIntroduction to Decision Analysis
•The field of decision analysis provides a framework for
making important decisions.
•Decision analysis allows us to select a decision from a set of
possible decision alternatives when uncertainties regarding
the future exist.
The goal is to optimize the resulting payoff in terms of a
decision criterion.
Example
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•Maximizing expected profit is a common criterion when
probabilities can be assessed.
•Maximizing the decision maker’s utility function is the mechanism
used when risk is factored into the decision making process.
Criteria Criteria
•Maximizing expected profit is a common criterion when
probabilities can be assessed.
•Maximizing the decision maker’s utility function is the mechanism
used when risk is factored into the decision making process.
Criteria Criteria
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Payoff Table AnalysisPayoff Table Analysis
•Payoff Tables
Application: Tom Brown Investment Decision
Tom Brown has inherited $1000 from a distant relative. Since he still has
another year of studies before graduation from Iowa State University, Tom
has decided to invest the $1000 for a year. Literally tens of thousands of
different investment possibilities are available to him, including growth
stocks, income stocks, corporate bonds, municipal bonds, government
bonds, futures, limited partnerships, annuities, and bank accounts.
Given the limited amount of money he has to invest, Tom has decided that it is
not worthwhile to spend the countless hours required to fully understand
those various investments. Therefore he has turned to a broker for
investment guidance.
Payoff Table AnalysisPayoff Table Analysis
•Payoff Tables
Application: Tom Brown Investment Decision
Tom Brown has inherited $1000 from a distant relative. Since he still has
another year of studies before graduation from Iowa State University, Tom
has decided to invest the $1000 for a year. Literally tens of thousands of
different investment possibilities are available to him, including growth
stocks, income stocks, corporate bonds, municipal bonds, government
bonds, futures, limited partnerships, annuities, and bank accounts.
Given the limited amount of money he has to invest, Tom has decided that it is
not worthwhile to spend the countless hours required to fully understand
those various investments. Therefore he has turned to a broker for
investment guidance.
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The broker has selected five potential investments she believes would be
appropriate for Tom: gold, a junk bond, a growth stock, a certificate of deposit
and a stock option hedge. Tom would like to set up a payoff table to help him
choose the appropriate investment.
The broker has selected five potential investments she believes would be
appropriate for Tom: gold, a junk bond, a growth stock, a certificate of deposit
and a stock option hedge. Tom would like to set up a payoff table to help him
choose the appropriate investment.
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Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The Payoff TableThe Payoff Table
The states of nature are mutually
exclusive and collectively exhaustive.
Define the states of nature.
DJA is down more
than 800 points
DJA is down
[-300, -800]
DJA moves
within
[-300,+300]
DJA is up
[+300,+1000]
DJA is up more
than1000 points
Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The Payoff TableThe Payoff Table
The states of nature are mutually
exclusive and collectively exhaustive.
Define the states of nature.
DJA is down more
than 800 points
DJA is down
[-300, -800]
DJA moves
within
[-300,+300]
DJA is up
[+300,+1000]
DJA is up more
than1000 points
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Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The Payoff TableThe Payoff Table
Determine the
set of possible
decision
alternatives.
Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The Payoff TableThe Payoff Table
Determine the
set of possible
decision
alternatives.
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Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The stock option alternative is dominated by the
bond alternative
250 200 150 -100 -150
-150
The Payoff TableThe Payoff Table
Decision States of Nature
AlternativesLarge RiseSmall RiseNo ChangeSmall FallLarge Fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D account 60 60 60 60 60
Stock option200 150 150 -200 -150
The stock option alternative is dominated by the
bond alternative
250 200 150 -100 -150
-150
The Payoff TableThe Payoff Table
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Classifying Decision Making CriteriaClassifying Decision Making Criteria
–Decision making under certainty.
•The future state-of-nature is assumed known.
•Example
–Decision making under risk.
•There is some knowledge of the probability of the states of
nature occurring.
-Decision making under uncertainty.
•There is no knowledge about the probability of the states of
nature occurring.
Classifying Decision Making CriteriaClassifying Decision Making Criteria
–Decision making under certainty.
•The future state-of-nature is assumed known.
•Example
–Decision making under risk.
•There is some knowledge of the probability of the states of
nature occurring.
-Decision making under uncertainty.
•There is no knowledge about the probability of the states of
nature occurring.
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•The decision criteria are based on the decision maker’s
attitude toward life.
•The criteria include the
–Maximin Criterion - pessimistic or conservative approach.
–Minimax Regret Criterion - pessimistic or conservative approach.
–Maximax Criterion - optimistic or aggressive approach.
–Principle of Insufficient Reasoning – no information about the
likelihood of the various states of nature.
Decision Making Under UncertaintyDecision Making Under Uncertainty
•The decision criteria are based on the decision maker’s
attitude toward life.
•The criteria include the
–Maximin Criterion - pessimistic or conservative approach.
–Minimax Regret Criterion - pessimistic or conservative approach.
–Maximax Criterion - optimistic or aggressive approach.
–Principle of Insufficient Reasoning – no information about the
likelihood of the various states of nature.
Decision Making Under UncertaintyDecision Making Under Uncertainty
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•This criterion is based on the worst-case scenario.
–It fits both a pessimistic and a conservative decision
maker’s styles.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximin CriterionThe Maximin Criterion
•This criterion is based on the worst-case scenario.
–It fits both a pessimistic and a conservative decision
maker’s styles.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximin CriterionThe Maximin Criterion
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TOM BROWN - The Maximin CriterionTOM BROWN - The Maximin Criterion
The Maximin Criterion Minimum
Decisions Large Rise Small rise No Change Small Fall Large FallPayoff
Gold -100 100 200 300 0 -100
Bond 250 200 150 -100-150-150
Stock 500 250 100 -200-600-600
C/D account 60 60 60 60 60 60
The Maximin Criterion Minimum
Decisions Large Rise Small rise No Change Small Fall Large FallPayoff
Gold -100 100 200 300 0 -100
Bond 250 200 150 -100-150-150
Stock 500 250 100 -200-600-600
C/D account 60 60 60 60 60 60
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TOM BROWN - The Maximin CriterionTOM BROWN - The Maximin Criterion
The Maximin Criterion Minimum
Decisions Large Rise Small rise No Change Small Fall Large FallPayoff
Gold -100 100 200 300 0 -100
Bond 250 200 150 -100-150-150
Stock 500 250 100 -200-600-600
C/D account 60 60 60 60 60 60
The Maximin Criterion Minimum
Decisions Large Rise Small rise No Change Small Fall Large FallPayoff
Gold -100 100 200 300 0 -100
Bond 250 200 150 -100-150-150
Stock 500 250 100 -200-600-600
C/D account 60 60 60 60 60 60
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Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
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• The Minimax Regret Criterion
–This criterion fits both a pessimistic and a
conservative decision maker approach.
–The payoff table is based on “lost opportunity,” or
“regret.”
–The decision maker incurs regret by failing to choose
the “best” decision.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
• The Minimax Regret Criterion
–This criterion fits both a pessimistic and a
conservative decision maker approach.
–The payoff table is based on “lost opportunity,” or
“regret.”
–The decision maker incurs regret by failing to choose
the “best” decision.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
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•The Minimax Regret Criterion
–To find an optimal decision, for each state of nature:
•Determine the best payoff over all decisions.
•Calculate the regret for each decision alternative as the
difference between its payoff value and this best payoff
value.
–For each decision find the maximum regret over all
states of nature.
–Select the decision alternative that has the minimum of
these “maximum regrets.”
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
•The Minimax Regret Criterion
–To find an optimal decision, for each state of nature:
•Determine the best payoff over all decisions.
•Calculate the regret for each decision alternative as the
difference between its payoff value and this best payoff
value.
–For each decision find the maximum regret over all
states of nature.
–Select the decision alternative that has the minimum of
these “maximum regrets.”
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Minimax Regret CriterionThe Minimax Regret Criterion
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The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
TOM BROWN – Regret TableTOM BROWN – Regret Table
Let us build the Regret Table
The Regret Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold 600 150 0 0 60
Bond 250 50 50 400 210
Stock 0 0 100 500 660
C/D 440 190 140 240 0
Investing in Stock generates no
regret when the market exhibits
a large rise
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
TOM BROWN – Regret TableTOM BROWN – Regret Table
Let us build the Regret Table
The Regret Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold 600 150 0 0 60
Bond 250 50 50 400 210
Stock 0 0 100 500 660
C/D 440 190 140 240 0
Investing in Stock generates no
regret when the market exhibits
a large rise
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The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Regret Table Maximum
Decision Large riseSmall riseNo changeSmall fallLarge fallRegret
Gold 600 150 0 0 60 600
Bond 250 50 50 400 210 400
Stock 0 0 100 500 660 660
C/D 440 190 140 240 0 440
The Regret Table Maximum
Decision Large riseSmall riseNo changeSmall fallLarge fallRegret
Gold 600 150 0 0 60 600
Bond 250 50 50 400 210 400
Stock 0 0 100 500 660 660
C/D 440 190 140 240 0 440
Investing in gold generates a regret
of 600 when the market exhibits
a large rise
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500 – (-100) = 600
TOM BROWN – Regret TableTOM BROWN – Regret Table
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Payoff Table
Decision Large riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
The Regret Table Maximum
Decision Large riseSmall riseNo changeSmall fallLarge fallRegret
Gold 600 150 0 0 60 600
Bond 250 50 50 400 210 400
Stock 0 0 100 500 660 660
C/D 440 190 140 240 0 440
The Regret Table Maximum
Decision Large riseSmall riseNo changeSmall fallLarge fallRegret
Gold 600 150 0 0 60 600
Bond 250 50 50 400 210 400
Stock 0 0 100 500 660 660
C/D 440 190 140 240 0 440
Investing in gold generates a regret
of 600 when the market exhibits
a large rise
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500 – (-100) = 600
TOM BROWN – Regret TableTOM BROWN – Regret Table
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•This criterion is based on the best possible scenario.
It fits both an optimistic and an aggressive decision maker.
•An optimistic decision maker believes that the best possible
outcome will always take place regardless of the decision
made.
•An aggressive decision maker looks for the decision with the
highest payoff (when payoff is profit).
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximax CriterionThe Maximax Criterion
•This criterion is based on the best possible scenario.
It fits both an optimistic and an aggressive decision maker.
•An optimistic decision maker believes that the best possible
outcome will always take place regardless of the decision
made.
•An aggressive decision maker looks for the decision with the
highest payoff (when payoff is profit).
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximax CriterionThe Maximax Criterion
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•To find an optimal decision.
–Find the maximum payoff for each decision
alternative.
–Select the decision alternative that has the maximum
of the “maximum” payoff.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximax CriterionThe Maximax Criterion
•To find an optimal decision.
–Find the maximum payoff for each decision
alternative.
–Select the decision alternative that has the maximum
of the “maximum” payoff.
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Maximax CriterionThe Maximax Criterion
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TOM BROWN -TOM BROWN - The Maximax CriterionThe Maximax Criterion
The Maximax Criterion Maximum
DecisionLarge riseSmall riseNo changeSmall fallLarge fallPayoff
Gold -100 100 200 300 0 300
Bond 250 200 150 -100-150 200
Stock 500 250 100 -200-600 500
C/D 60 60 60 60 60 60
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TOM BROWN -TOM BROWN - The Maximax CriterionThe Maximax Criterion
The Maximax Criterion Maximum
DecisionLarge riseSmall riseNo changeSmall fallLarge fallPayoff
Gold -100 100 200 300 0 300
Bond 250 200 150 -100-150 200
Stock 500 250 100 -200-600 500
C/D 60 60 60 60 60 60
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•This criterion might appeal to a decision maker who
is neither pessimistic nor optimistic.
– It assumes all the states of nature are equally likely to
occur.
–The procedure to find an optimal decision.
•For each decision add all the payoffs.
•Select the decision with the largest sum (for profits).
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Principle of Insufficient ReasonThe Principle of Insufficient Reason
•This criterion might appeal to a decision maker who
is neither pessimistic nor optimistic.
– It assumes all the states of nature are equally likely to
occur.
–The procedure to find an optimal decision.
•For each decision add all the payoffs.
•Select the decision with the largest sum (for profits).
Decision Making Under Uncertainty - Decision Making Under Uncertainty -
The Principle of Insufficient ReasonThe Principle of Insufficient Reason
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TOM BROWNTOM BROWN - - Insufficient ReasonInsufficient Reason
• Sum of Payoffs
–Gold600 Dollars
–Bond350 Dollars
–Stock 50 Dollars
–C/D300 Dollars
•Based on this criterion the optimal decision
alternative is to invest in gold.
TOM BROWNTOM BROWN - - Insufficient ReasonInsufficient Reason
• Sum of Payoffs
–Gold600 Dollars
–Bond350 Dollars
–Stock 50 Dollars
–C/D300 Dollars
•Based on this criterion the optimal decision
alternative is to invest in gold.
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Decision Making Under RiskDecision Making Under Risk
•The probability estimate for the occurrence of
each state of nature (if available) can be
incorporated in the search for the optimal
decision.
•For each decision calculate its expected payoff.
Decision Making Under RiskDecision Making Under Risk
•The probability estimate for the occurrence of
each state of nature (if available) can be
incorporated in the search for the optimal
decision.
•For each decision calculate its expected payoff.
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Decision Making Under Risk –Decision Making Under Risk –
The Expected Value CriterionThe Expected Value Criterion
Expected Payoff = (Probability)(Payoff)
•For each decision calculate the expected payoff
as follows:
(The summation is calculated across all the states of nature)
•Select the decision with the best expected payoff
Decision Making Under Risk –Decision Making Under Risk –
The Expected Value CriterionThe Expected Value Criterion
Expected Payoff = (Probability)(Payoff)
•For each decision calculate the expected payoff
as follows:
(The summation is calculated across all the states of nature)
•Select the decision with the best expected payoff
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TOM BROWN -TOM BROWN - The Expected Value CriterionThe Expected Value Criterion
The Expected Value Criterion Expected
DecisionLarge riseSmall riseNo changeSmall fallLarge fallValue
Gold -100 100 200 300 0 100
Bond 250 200 150 -100-150 130
Stock 500 250 100 -200-600 125
C/D 60 60 60 60 60 60
Prior Prob.0.2 0.3 0.3 0.1 0.1
EV = (0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130
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TOM BROWN -TOM BROWN - The Expected Value CriterionThe Expected Value Criterion
The Expected Value Criterion Expected
DecisionLarge riseSmall riseNo changeSmall fallLarge fallValue
Gold -100 100 200 300 0 100
Bond 250 200 150 -100-150 130
Stock 500 250 100 -200-600 125
C/D 60 60 60 60 60 60
Prior Prob.0.2 0.3 0.3 0.1 0.1
EV = (0.2)(250) + (0.3)(200) + (0.3)(150) + (0.1)(-100) + (0.1)(-150) = 130
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•The expected value criterion is useful generally
in two cases:
–Long run planning is appropriate, and decision
situations repeat themselves.
–The decision maker is risk neutral.
When to use the expected value When to use the expected value
approachapproach
•The expected value criterion is useful generally
in two cases:
–Long run planning is appropriate, and decision
situations repeat themselves.
–The decision maker is risk neutral.
When to use the expected value When to use the expected value
approachapproach
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Expected Regret CriterionExpected Regret Criterion
Expected Regret Approach
1.Determine the best value (maximum payoff or minimum cost) for each
states of nature
2.For each state of nature, the regret corresponding to a decision
alternative is the difference between its payoff value and this best value.
3.Find the expected regret for each decision alternative
4.Select the decision alternative that has the maximum expected regret.
Expected Regret CriterionExpected Regret Criterion
Expected Regret Approach
1.Determine the best value (maximum payoff or minimum cost) for each
states of nature
2.For each state of nature, the regret corresponding to a decision
alternative is the difference between its payoff value and this best value.
3.Find the expected regret for each decision alternative
4.Select the decision alternative that has the maximum expected regret.
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Applications-6.3Applications-6.3
National foods has developed a new sports beverage it would like to advertise on National foods has developed a new sports beverage it would like to advertise on
Super Bowl Sunday. National’s advertising agency can purchase either one, two.or Super Bowl Sunday. National’s advertising agency can purchase either one, two.or
three 30 second commercials advertising the drink. It estimates that the return will be three 30 second commercials advertising the drink. It estimates that the return will be
based on super Bowl viewer ship, which in turn based on fans’ perception on whether based on super Bowl viewer ship, which in turn based on fans’ perception on whether
the game is dull, average, above average, or exciting. the game is dull, average, above average, or exciting.
National foods ad agency has constructed the following payoff table giving its National foods ad agency has constructed the following payoff table giving its
estimate of the expected profit (in $100,000’s ) returning from purchasing one, two or estimate of the expected profit (in $100,000’s ) returning from purchasing one, two or
three advertising spots. (Another possible decision is for National foods not to three advertising spots. (Another possible decision is for National foods not to
advertise at all during the Super Bowl). The States of nature of the game being “dull”, advertise at all during the Super Bowl). The States of nature of the game being “dull”,
“average”, “ above average” or “exciting”.“average”, “ above average” or “exciting”.
Applications-6.3Applications-6.3
National foods has developed a new sports beverage it would like to advertise on National foods has developed a new sports beverage it would like to advertise on
Super Bowl Sunday. National’s advertising agency can purchase either one, two.or Super Bowl Sunday. National’s advertising agency can purchase either one, two.or
three 30 second commercials advertising the drink. It estimates that the return will be three 30 second commercials advertising the drink. It estimates that the return will be
based on super Bowl viewer ship, which in turn based on fans’ perception on whether based on super Bowl viewer ship, which in turn based on fans’ perception on whether
the game is dull, average, above average, or exciting. the game is dull, average, above average, or exciting.
National foods ad agency has constructed the following payoff table giving its National foods ad agency has constructed the following payoff table giving its
estimate of the expected profit (in $100,000’s ) returning from purchasing one, two or estimate of the expected profit (in $100,000’s ) returning from purchasing one, two or
three advertising spots. (Another possible decision is for National foods not to three advertising spots. (Another possible decision is for National foods not to
advertise at all during the Super Bowl). The States of nature of the game being “dull”, advertise at all during the Super Bowl). The States of nature of the game being “dull”,
“average”, “ above average” or “exciting”.“average”, “ above average” or “exciting”.
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__________________________________________________________________________________________________________________________________________
Number of 30 Perceived Game ExcitementNumber of 30 Perceived Game Excitement
Sec. Commercials ______________________________________ Sec. Commercials ______________________________________
Purchased Dull Average Above exciting Purchased Dull Average Above exciting
average average
____________________________________________________________________________________________________________________________________________
One -2 3 7 13One -2 3 7 13
Two -5 6 12 18Two -5 6 12 18
Three -9 5 13 22Three -9 5 13 22
______________________________________________________________________________________________________________________________________________
a.a.What is the optimal decision if the national foods ad manager is optimisticWhat is the optimal decision if the national foods ad manager is optimistic
b.b.What is the optimal decision if the national Foods advertising manager is What is the optimal decision if the national Foods advertising manager is
pessimisticpessimistic
c.c.What is the optimal decision if the National Foods ad manager wishes the minimize What is the optimal decision if the National Foods ad manager wishes the minimize
the firm’s maximum regret?the firm’s maximum regret?
__________________________________________________________________________________________________________________________________________
Number of 30 Perceived Game ExcitementNumber of 30 Perceived Game Excitement
Sec. Commercials ______________________________________ Sec. Commercials ______________________________________
Purchased Dull Average Above exciting Purchased Dull Average Above exciting
average average
____________________________________________________________________________________________________________________________________________
One -2 3 7 13One -2 3 7 13
Two -5 6 12 18Two -5 6 12 18
Three -9 5 13 22Three -9 5 13 22
______________________________________________________________________________________________________________________________________________
a.a.What is the optimal decision if the national foods ad manager is optimisticWhat is the optimal decision if the national foods ad manager is optimistic
b.b.What is the optimal decision if the national Foods advertising manager is What is the optimal decision if the national Foods advertising manager is
pessimisticpessimistic
c.c.What is the optimal decision if the National Foods ad manager wishes the minimize What is the optimal decision if the National Foods ad manager wishes the minimize
the firm’s maximum regret?the firm’s maximum regret?
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Consider the data given in problem 3 for national Foods. Based on passed super bowl Consider the data given in problem 3 for national Foods. Based on passed super bowl
games, suppose the Decision maker believes that the following probabilities hold games, suppose the Decision maker believes that the following probabilities hold
for the states of nature.for the states of nature.
P(Dull Game)=0.20P(Dull Game)=0.20
P(Average Game)=.40P(Average Game)=.40
P(Above Average game)=.30P(Above Average game)=.30
P(exciting)=0.10P(exciting)=0.10
a.a.Using the expected value criterion, determine how many commercials National Using the expected value criterion, determine how many commercials National
Foods should purchase?Foods should purchase?
b.b.Based on the probabilities given here, determine the expected value of perfect Based on the probabilities given here, determine the expected value of perfect
information. information.
Consider the data given in problem 3 for national Foods. Based on passed super bowl Consider the data given in problem 3 for national Foods. Based on passed super bowl
games, suppose the Decision maker believes that the following probabilities hold games, suppose the Decision maker believes that the following probabilities hold
for the states of nature.for the states of nature.
P(Dull Game)=0.20P(Dull Game)=0.20
P(Average Game)=.40P(Average Game)=.40
P(Above Average game)=.30P(Above Average game)=.30
P(exciting)=0.10P(exciting)=0.10
a.a.Using the expected value criterion, determine how many commercials National Using the expected value criterion, determine how many commercials National
Foods should purchase?Foods should purchase?
b.b.Based on the probabilities given here, determine the expected value of perfect Based on the probabilities given here, determine the expected value of perfect
information. information.
31
Expected Value of Perfect InformationExpected Value of Perfect Information
•The gain in expected return obtained from knowing
with certainty the future state of nature is called:
Expected Value of Perfect Information Expected Value of Perfect Information
(EVPI)(EVPI)
Expected Value of Perfect InformationExpected Value of Perfect Information
•The gain in expected return obtained from knowing
with certainty the future state of nature is called:
Expected Value of Perfect Information Expected Value of Perfect Information
(EVPI)(EVPI)
32
Expected Value of Perfect InformationExpected Value of Perfect Information
decision
making prior tooccur will
nature of state which to
asn informatio additional
houtreturn wit Expected
decision making
prior tooccur will
nature of state which to
asn informatioperfect
hreturn wit Expected
nInformatio
Perfect of value
Expected
Expected Value of Perfect InformationExpected Value of Perfect Information
decision
making prior tooccur will
nature of state which to
asn informatio additional
houtreturn wit Expected
decision making
prior tooccur will
nature of state which to
asn informatioperfect
hreturn wit Expected
nInformatio
Perfect of value
Expected
33
The Expected Value of Perfect Information
DecisionLarge riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
Probab. 0.2 0.3 0.3 0.1 0.1
If it were known with certainty that there will be a “Large Rise” in the market
Large rise
... the optimal decision would be to invest in...
-100
250
500
60
Stock
Similarly,…
TOM BROWN -TOM BROWN - EVPIEVPI
The Expected Value of Perfect Information
DecisionLarge riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
Probab. 0.2 0.3 0.3 0.1 0.1
If it were known with certainty that there will be a “Large Rise” in the market
Large rise
... the optimal decision would be to invest in...
-100
250
500
60
Stock
Similarly,…
TOM BROWN -TOM BROWN - EVPIEVPI
34
The Expected Value of Perfect Information
DecisionLarge riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
Probab. 0.2 0.3 0.3 0.1 0.1
-100
250
500
60
Expected Return with Perfect information =
ERPI = 0.2(500)+0.3(250)+0.3(200)+0.1(300)+0.1(60) = $271
Expected Return without additional information =
Expected Return of the EV criterion = $130
EVPI = ERPI - EREV = $271 - $130 = $141
TOM BROWN -TOM BROWN - EVPIEVPI
The Expected Value of Perfect Information
DecisionLarge riseSmall riseNo changeSmall fallLarge fall
Gold -100 100 200 300 0
Bond 250 200 150 -100 -150
Stock 500 250 100 -200 -600
C/D 60 60 60 60 60
Probab. 0.2 0.3 0.3 0.1 0.1
-100
250
500
60
Expected Return with Perfect information =
ERPI = 0.2(500)+0.3(250)+0.3(200)+0.1(300)+0.1(60) = $271
Expected Return without additional information =
Expected Return of the EV criterion = $130
EVPI = ERPI - EREV = $271 - $130 = $141
TOM BROWN -TOM BROWN - EVPIEVPI
35
Bayesian Analysis - Decision Making Bayesian Analysis - Decision Making
with Imperfect Informationwith Imperfect Information
•Bayesian Statistics play a role in assessing
additional information obtained from various
sources.
•This additional information may assist in refining
original probability estimates, and help improve
decision making.
Bayesian Analysis - Decision Making Bayesian Analysis - Decision Making
with Imperfect Informationwith Imperfect Information
•Bayesian Statistics play a role in assessing
additional information obtained from various
sources.
•This additional information may assist in refining
original probability estimates, and help improve
decision making.
36
Tom Brown Investment Decision (Continued)Tom Brown Investment Decision (Continued)
Tom has learned that, for only $50, he can receive the results of noted Tom has learned that, for only $50, he can receive the results of noted
economist Milton Samuelman’s multimillion dollar economic economist Milton Samuelman’s multimillion dollar economic
forecast, which predicts either “positive” or “negative” economic forecast, which predicts either “positive” or “negative” economic
growth for the upcoming year. Samuelman has offered the following growth for the upcoming year. Samuelman has offered the following
variable statistics regarding the results of his model:variable statistics regarding the results of his model:
1.1.When the stock market showed the large rise, the forecast predicted When the stock market showed the large rise, the forecast predicted
“positive” 80% of the time and “negative” 20% of the time.“positive” 80% of the time and “negative” 20% of the time.
2.2.When the stock market showed a small rise, the forecast predicted When the stock market showed a small rise, the forecast predicted
“positive” 70% of the time and “negative” 30% of the time.“positive” 70% of the time and “negative” 30% of the time.
3.3.When the stock market showed no change , the forecast was equally When the stock market showed no change , the forecast was equally
likely to predict “positive” or “negative”.likely to predict “positive” or “negative”.
4.4.When the stock market showed a small fall, the forecast predicted When the stock market showed a small fall, the forecast predicted
“positive” 40% of the time and negative 60% of the time.“positive” 40% of the time and negative 60% of the time.
5.5.When the stock market showed a large fall, the forecast always When the stock market showed a large fall, the forecast always
Tom Brown Investment Decision (Continued)Tom Brown Investment Decision (Continued)
Tom has learned that, for only $50, he can receive the results of noted Tom has learned that, for only $50, he can receive the results of noted
economist Milton Samuelman’s multimillion dollar economic economist Milton Samuelman’s multimillion dollar economic
forecast, which predicts either “positive” or “negative” economic forecast, which predicts either “positive” or “negative” economic
growth for the upcoming year. Samuelman has offered the following growth for the upcoming year. Samuelman has offered the following
variable statistics regarding the results of his model:variable statistics regarding the results of his model:
1.1.When the stock market showed the large rise, the forecast predicted When the stock market showed the large rise, the forecast predicted
“positive” 80% of the time and “negative” 20% of the time.“positive” 80% of the time and “negative” 20% of the time.
2.2.When the stock market showed a small rise, the forecast predicted When the stock market showed a small rise, the forecast predicted
“positive” 70% of the time and “negative” 30% of the time.“positive” 70% of the time and “negative” 30% of the time.
3.3.When the stock market showed no change , the forecast was equally When the stock market showed no change , the forecast was equally
likely to predict “positive” or “negative”.likely to predict “positive” or “negative”.
4.4.When the stock market showed a small fall, the forecast predicted When the stock market showed a small fall, the forecast predicted
“positive” 40% of the time and negative 60% of the time.“positive” 40% of the time and negative 60% of the time.
5.5.When the stock market showed a large fall, the forecast always When the stock market showed a large fall, the forecast always
37
Predicted “negative”Predicted “negative”
Tom would like to know whether it is worthwhile to pay $50 for the Tom would like to know whether it is worthwhile to pay $50 for the
result of the Samuelman forecast.result of the Samuelman forecast.
Predicted “negative”Predicted “negative”
Tom would like to know whether it is worthwhile to pay $50 for the Tom would like to know whether it is worthwhile to pay $50 for the
result of the Samuelman forecast.result of the Samuelman forecast.
38
•If the expected gain resulting from the decisions made
with the forecast exceeds $50, Tom should purchase
the forecast.
The expected gain =
Expected payoff with forecast – EREV
•To find Expected payoff with forecast Tom should
determine what to do when:
–The forecast is “positive growth”,
–The forecast is “negative growth”.
TOM BROWN – SolutionTOM BROWN – Solution
Using Sample InformationUsing Sample Information
•If the expected gain resulting from the decisions made
with the forecast exceeds $50, Tom should purchase
the forecast.
The expected gain =
Expected payoff with forecast – EREV
•To find Expected payoff with forecast Tom should
determine what to do when:
–The forecast is “positive growth”,
–The forecast is “negative growth”.
TOM BROWN – SolutionTOM BROWN – Solution
Using Sample InformationUsing Sample Information
39
Conditional ProbabilitiesConditional Probabilities
P(forecast predicts”positive”/large rise in the market)=0.80P(forecast predicts”positive”/large rise in the market)=0.80
P(forecast predicts “ negative”/large rise in the market)=0.20P(forecast predicts “ negative”/large rise in the market)=0.20
P(forecast predicts ‘positive”/ small rise in the market)=0.70P(forecast predicts ‘positive”/ small rise in the market)=0.70
P(forecast predicts “negative”/small rise in the market)=0.30P(forecast predicts “negative”/small rise in the market)=0.30
P(forecast predicts “positive”/ no change in the market)=0.50P(forecast predicts “positive”/ no change in the market)=0.50
P(forecast predicts “negative”/ no change in the market) =0.50P(forecast predicts “negative”/ no change in the market) =0.50
P (forecast predicts “positive”/ small fall in the market)=0.40P (forecast predicts “positive”/ small fall in the market)=0.40
P(forecast predicts “ negative” / small fall in the market)=0.60P(forecast predicts “ negative” / small fall in the market)=0.60
P(forecast predicts ‘positive”/ large fall in the market)=0P(forecast predicts ‘positive”/ large fall in the market)=0
P(forecast predicts “negative”/large fall in the market)=1.00P(forecast predicts “negative”/large fall in the market)=1.00
Conditional ProbabilitiesConditional Probabilities
P(forecast predicts”positive”/large rise in the market)=0.80P(forecast predicts”positive”/large rise in the market)=0.80
P(forecast predicts “ negative”/large rise in the market)=0.20P(forecast predicts “ negative”/large rise in the market)=0.20
P(forecast predicts ‘positive”/ small rise in the market)=0.70P(forecast predicts ‘positive”/ small rise in the market)=0.70
P(forecast predicts “negative”/small rise in the market)=0.30P(forecast predicts “negative”/small rise in the market)=0.30
P(forecast predicts “positive”/ no change in the market)=0.50P(forecast predicts “positive”/ no change in the market)=0.50
P(forecast predicts “negative”/ no change in the market) =0.50P(forecast predicts “negative”/ no change in the market) =0.50
P (forecast predicts “positive”/ small fall in the market)=0.40P (forecast predicts “positive”/ small fall in the market)=0.40
P(forecast predicts “ negative” / small fall in the market)=0.60P(forecast predicts “ negative” / small fall in the market)=0.60
P(forecast predicts ‘positive”/ large fall in the market)=0P(forecast predicts ‘positive”/ large fall in the market)=0
P(forecast predicts “negative”/large fall in the market)=1.00P(forecast predicts “negative”/large fall in the market)=1.00
40
•Tom needs to know the following probabilities
–P(Large rise | The forecast predicted “Positive”)
–P(Small rise | The forecast predicted “Positive”)
–P(No change | The forecast predicted “Positive ”)
–P(Small fall | The forecast predicted “Positive”)
–P(Large Fall | The forecast predicted “Positive”)
–P(Large rise | The forecast predicted “Negative ”)
–P(Small rise | The forecast predicted “Negative”)
–P(No change | The forecast predicted “Negative”)
–P(Small fall | The forecast predicted “Negative”)
–P(Large Fall) | The forecast predicted “Negative”)
TOM BROWN – SolutionTOM BROWN – Solution
Using Sample InformationUsing Sample Information
•Tom needs to know the following probabilities
–P(Large rise | The forecast predicted “Positive”)
–P(Small rise | The forecast predicted “Positive”)
–P(No change | The forecast predicted “Positive ”)
–P(Small fall | The forecast predicted “Positive”)
–P(Large Fall | The forecast predicted “Positive”)
–P(Large rise | The forecast predicted “Negative ”)
–P(Small rise | The forecast predicted “Negative”)
–P(No change | The forecast predicted “Negative”)
–P(Small fall | The forecast predicted “Negative”)
–P(Large Fall) | The forecast predicted “Negative”)
TOM BROWN – SolutionTOM BROWN – Solution
Using Sample InformationUsing Sample Information
41
•Bayes’ Theorem provides a procedure to calculate
these probabilities
P(B|A
i
)P(A
i
)
P(B|A
1
)P(A
1
)+ P(B|A
2
)P(A
2
)+…+ P(B|A
n
)P(A
n
)
P(A
i|B) =
Posterior Probabilities
Probabilities determined
after the additional info
becomes available.
TOM BROWN – SolutionTOM BROWN – Solution
Bayes’ TheoremBayes’ Theorem
Prior probabilities
Probability estimates
determined based on
current info, before the
new info becomes available.
•Bayes’ Theorem provides a procedure to calculate
these probabilities
P(B|A
i
)P(A
i
)
P(B|A
1
)P(A
1
)+ P(B|A
2
)P(A
2
)+…+ P(B|A
n
)P(A
n
)
P(A
i|B) =
Posterior Probabilities
Probabilities determined
after the additional info
becomes available.
TOM BROWN – SolutionTOM BROWN – Solution
Bayes’ TheoremBayes’ Theorem
Prior probabilities
Probability estimates
determined based on
current info, before the
new info becomes available.
42
Posterior Probability “ Positive” Posterior Probability “ Positive”
Forecast for Tom BrownForecast for Tom Brown
States of nature Prior
Probability
P(Si)
Conditional
Probability
P(positive/Si)
Joint Probability
P(positive Si)
P(Si/positive)
LR 0.20 0.80 0.16 0.286
SR 0.30 0.70 0.21 0.375
NC 0.30 0.50 0.15 0.268
SF 0.10 0.40 0.04 0.071
LF 0.10 0 0 0
Total 0.56
i
S
P(positive)=0.56P(positive)=0.56
Posterior Probability “ Positive” Posterior Probability “ Positive”
Forecast for Tom BrownForecast for Tom Brown
States of nature Prior
Probability
P(Si)
Conditional
Probability
P(positive/Si)
Joint Probability
P(positive Si)
P(Si/positive)
LR 0.20 0.80 0.16 0.286
SR 0.30 0.70 0.21 0.375
NC 0.30 0.50 0.15 0.268
SF 0.10 0.40 0.04 0.071
LF 0.10 0 0 0
Total 0.56
i
S
P(positive)=0.56P(positive)=0.56
43
Posterior Probability: “negative” Posterior Probability: “negative”
forecast for Tom Brownforecast for Tom Brown
States of nature SiPrior probability
P(si)
Condl Probability
P(negative/Si)
Joint Probability
P(negative
Si)
P(si/ negative)
LS 0.20 0.20 0.04 0.091
SR 0.30 0.30 0.09 0.205
NC 0.30 0.50 0.15 0.341
SF 0.10 0.60 0.06 0.136
LF 0.10 1.00 0.10 0.227
Total 0.44
Posterior Probability: “negative” Posterior Probability: “negative”
forecast for Tom Brownforecast for Tom Brown
States of nature SiPrior probability
P(si)
Condl Probability
P(negative/Si)
Joint Probability
P(negative
Si)
P(si/ negative)
LS 0.20 0.20 0.04 0.091
SR 0.30 0.30 0.09 0.205
NC 0.30 0.50 0.15 0.341
SF 0.10 0.60 0.06 0.136
LF 0.10 1.00 0.10 0.227
Total 0.44
44
Expected value of sample informtionExpected value of sample informtion
If the Samuelman’s Forecast is positive economic growth, the revised expected values for the If the Samuelman’s Forecast is positive economic growth, the revised expected values for the
decision alternatives (rounded to the nearest dollar) aredecision alternatives (rounded to the nearest dollar) are
EV(gold/”positive”)=$84EV(gold/”positive”)=$84
EV(Bond/’Positive)=$180EV(Bond/’Positive)=$180
EV(Stock/”Positive”)=$249EV(Stock/”Positive”)=$249
EV(C/D/”Positive”)=$60EV(C/D/”Positive”)=$60
Decision: So if the samuelman’s forecast is positive then buying the stock would be optimal. Decision: So if the samuelman’s forecast is positive then buying the stock would be optimal.
Expected value of sample informtionExpected value of sample informtion
If the Samuelman’s Forecast is positive economic growth, the revised expected values for the If the Samuelman’s Forecast is positive economic growth, the revised expected values for the
decision alternatives (rounded to the nearest dollar) aredecision alternatives (rounded to the nearest dollar) are
EV(gold/”positive”)=$84EV(gold/”positive”)=$84
EV(Bond/’Positive)=$180EV(Bond/’Positive)=$180
EV(Stock/”Positive”)=$249EV(Stock/”Positive”)=$249
EV(C/D/”Positive”)=$60EV(C/D/”Positive”)=$60
Decision: So if the samuelman’s forecast is positive then buying the stock would be optimal. Decision: So if the samuelman’s forecast is positive then buying the stock would be optimal.
45
Samuelman’s forecast is negativeSamuelman’s forecast is negative
The expected returns are The expected returns are
EV(Gold/ negative)=$120EV(Gold/ negative)=$120
EV( Bond/ negative )=$67EV( Bond/ negative )=$67
EV (Stock/ “negative”)=-$33EV (Stock/ “negative”)=-$33
EV(C/D/ “ Negative”)=$60EV(C/D/ “ Negative”)=$60
Samuelman’s forecast is negativeSamuelman’s forecast is negative
The expected returns are The expected returns are
EV(Gold/ negative)=$120EV(Gold/ negative)=$120
EV( Bond/ negative )=$67EV( Bond/ negative )=$67
EV (Stock/ “negative”)=-$33EV (Stock/ “negative”)=-$33
EV(C/D/ “ Negative”)=$60EV(C/D/ “ Negative”)=$60
46
Expected value of sample InformationExpected value of sample Information
ninformatio
samplewithout
return Expected
ninformatio samplewith
return Expected
nInformatio Sample of
Value Expected
EREV-ERSIEVSI
Expected value of sample InformationExpected value of sample Information
ninformatio
samplewithout
return Expected
ninformatio samplewith
return Expected
nInformatio Sample of
Value Expected
EREV-ERSIEVSI
47
DecisionDecision
ERSI=.56(249.11)+.44(120.45)=$192.50ERSI=.56(249.11)+.44(120.45)=$192.50
EREV=$130EREV=$130
EVSI=$192.50-130=$62.50EVSI=$192.50-130=$62.50
Decision: Tom should acquire itDecision: Tom should acquire it
DecisionDecision
ERSI=.56(249.11)+.44(120.45)=$192.50ERSI=.56(249.11)+.44(120.45)=$192.50
EREV=$130EREV=$130
EVSI=$192.50-130=$62.50EVSI=$192.50-130=$62.50
Decision: Tom should acquire itDecision: Tom should acquire it
48
Extension of Application 6.3Extension of Application 6.3
Consider the data given in problems (3 and 4 ) for National Foods. The firm can hire the Consider the data given in problems (3 and 4 ) for National Foods. The firm can hire the
noted sports pundit Jim Worden to give his opinion as to whether or not the Super Bowl noted sports pundit Jim Worden to give his opinion as to whether or not the Super Bowl
game will be interesting. Suppose the following probabilities holds for Jim’s game will be interesting. Suppose the following probabilities holds for Jim’s
predictions.predictions.
P(Jim Predicts game will be interesting /game is dull)=.15,P(Jim Predicts game will be interesting /game is dull)=.15,
P(Jim predicts game will be interesting / game is average).25P(Jim predicts game will be interesting / game is average).25
P(Jim predicts game will be interesting / game is above average)=.50,P(Jim predicts game will be interesting / game is above average)=.50,
P(Jim predicts game will be interesting / game is exciting)=.80,P(Jim predicts game will be interesting / game is exciting)=.80,
P(Jim predicts game will not be interesting / game is Dull)= .85P(Jim predicts game will not be interesting / game is Dull)= .85
P(Jim predicts game will not be interesting / game is average)= .75P(Jim predicts game will not be interesting / game is average)= .75
P(Jim predicts game will not be interesting / game is above average)=.50,P(Jim predicts game will not be interesting / game is above average)=.50,
P(Jim predicts game will not be interesting / game is exciting)=.20,P(Jim predicts game will not be interesting / game is exciting)=.20,
Extension of Application 6.3Extension of Application 6.3
Consider the data given in problems (3 and 4 ) for National Foods. The firm can hire the Consider the data given in problems (3 and 4 ) for National Foods. The firm can hire the
noted sports pundit Jim Worden to give his opinion as to whether or not the Super Bowl noted sports pundit Jim Worden to give his opinion as to whether or not the Super Bowl
game will be interesting. Suppose the following probabilities holds for Jim’s game will be interesting. Suppose the following probabilities holds for Jim’s
predictions.predictions.
P(Jim Predicts game will be interesting /game is dull)=.15,P(Jim Predicts game will be interesting /game is dull)=.15,
P(Jim predicts game will be interesting / game is average).25P(Jim predicts game will be interesting / game is average).25
P(Jim predicts game will be interesting / game is above average)=.50,P(Jim predicts game will be interesting / game is above average)=.50,
P(Jim predicts game will be interesting / game is exciting)=.80,P(Jim predicts game will be interesting / game is exciting)=.80,
P(Jim predicts game will not be interesting / game is Dull)= .85P(Jim predicts game will not be interesting / game is Dull)= .85
P(Jim predicts game will not be interesting / game is average)= .75P(Jim predicts game will not be interesting / game is average)= .75
P(Jim predicts game will not be interesting / game is above average)=.50,P(Jim predicts game will not be interesting / game is above average)=.50,
P(Jim predicts game will not be interesting / game is exciting)=.20,P(Jim predicts game will not be interesting / game is exciting)=.20,
49
QuestionsQuestions
a.a.If Jim predicts the game will be interesting what is the probability If Jim predicts the game will be interesting what is the probability
that the game will be dull.that the game will be dull.
b.b.What is the National’s optimal strategy if Jim predicts the game will What is the National’s optimal strategy if Jim predicts the game will
be (I) interesting (ii) Not interestingbe (I) interesting (ii) Not interesting
c.c.What is the expected value of Jim’s information.What is the expected value of Jim’s information.
QuestionsQuestions
a.a.If Jim predicts the game will be interesting what is the probability If Jim predicts the game will be interesting what is the probability
that the game will be dull.that the game will be dull.
b.b.What is the National’s optimal strategy if Jim predicts the game will What is the National’s optimal strategy if Jim predicts the game will
be (I) interesting (ii) Not interestingbe (I) interesting (ii) Not interesting
c.c.What is the expected value of Jim’s information.What is the expected value of Jim’s information.
50
•The revised expected values for each decision:
Positive forecastNegative forecast
EV(Gold|Positive) = 84EV(Gold|Negative) = 120
EV(Bond|Positive) = 180EV(Bond|Negative) = 65
EV(Stock|Positive) = 250 EV(Stock|Negative)
= -37
EV(C/D|Positive) = 60EV(C/D|Negative) = 60
If the forecast is “Positive”
Invest in Stock.
If the forecast is “Negative”
Invest in Gold.
TOM BROWN – Conditional Expected ValuesTOM BROWN – Conditional Expected Values
•The revised expected values for each decision:
Positive forecastNegative forecast
EV(Gold|Positive) = 84EV(Gold|Negative) = 120
EV(Bond|Positive) = 180EV(Bond|Negative) = 65
EV(Stock|Positive) = 250 EV(Stock|Negative)
= -37
EV(C/D|Positive) = 60EV(C/D|Negative) = 60
If the forecast is “Positive”
Invest in Stock.
If the forecast is “Negative”
Invest in Gold.
TOM BROWN – Conditional Expected ValuesTOM BROWN – Conditional Expected Values
51
•Since the forecast is unknown before it is
purchased, Tom can only calculate the expected
return from purchasing it.
•Expected return when buying the forecast = ERSI =
P(Forecast is positive)(EV(Stock|Forecast is positive)) +
P(Forecast is negative”)(EV(Gold|Forecast is negative))
= (.56)(250) + (.44)(120) = $192.5
TOM BROWN – Conditional Expected ValuesTOM BROWN – Conditional Expected Values
•Since the forecast is unknown before it is
purchased, Tom can only calculate the expected
return from purchasing it.
•Expected return when buying the forecast = ERSI =
P(Forecast is positive)(EV(Stock|Forecast is positive)) +
P(Forecast is negative”)(EV(Gold|Forecast is negative))
= (.56)(250) + (.44)(120) = $192.5
TOM BROWN – Conditional Expected ValuesTOM BROWN – Conditional Expected Values
52
•The expected gain from buying the forecast is:
EVSI = ERSI – EREV = 192.5 – 130 = $62.5
•Tom should purchase the forecast. His expected
gain is greater than the forecast cost.
•Efficiency = EVSI / EVPI = 63 / 141 = 0.45
Expected Value of Sampling Expected Value of Sampling
Information (EVSI)Information (EVSI)
•The expected gain from buying the forecast is:
EVSI = ERSI – EREV = 192.5 – 130 = $62.5
•Tom should purchase the forecast. His expected
gain is greater than the forecast cost.
•Efficiency = EVSI / EVPI = 63 / 141 = 0.45
Expected Value of Sampling Expected Value of Sampling
Information (EVSI)Information (EVSI)
DECISION TREE APPLICATIONDECISION TREE APPLICATION
•You have the chance to invest in three mutual
funds utility, aggressive growth and global. The
value of your investment will change depending on
the market conditions. There is a 10% chance the
market will go down, 50% chance it will remain
moderate , and 40% chance it will per form well.
The following table provides the percentage change
in the investment value under the three conditions
53
•You have the chance to invest in three mutual
funds utility, aggressive growth and global. The
value of your investment will change depending on
the market conditions. There is a 10% chance the
market will go down, 50% chance it will remain
moderate , and 40% chance it will per form well.
The following table provides the percentage change
in the investment value under the three conditions
53
CONTINUEDCONTINUED
PERSENT RETURN ON INVESTMENT
_______________________________
ALTERNATIVE DOWN MARKET (%) MODERATE MARKET (%) UP MARKET (%)
________________________________________________________________________________________
UTILITY +5 +7 +8
AGGREGATE GROWTH -10 +5 +30
GLOBAL +2 +7 +20
________________________________________________________________________________________
_
(A)REPRESENT THE PROBLEM AS A DECISION TREE.
(B) WHICH MUTUAL FUND SHOULD YOU SELECT?
54
PERSENT RETURN ON INVESTMENT
_______________________________
ALTERNATIVE DOWN MARKET (%) MODERATE MARKET (%) UP MARKET (%)
________________________________________________________________________________________
UTILITY +5 +7 +8
AGGREGATE GROWTH -10 +5 +30
GLOBAL +2 +7 +20
________________________________________________________________________________________
_
(A)REPRESENT THE PROBLEM AS A DECISION TREE.
(B) WHICH MUTUAL FUND SHOULD YOU SELECT?
54
APPLICATION DECISION TREEAPPLICATION DECISION TREE
•Farmer McCoy can plant either corn or soybean. The
probabilities that the next harvest prices of these commodities
will go up, stay the same or go down are .25, .30, and .45
respectively. If the prices go up corn crop will net $30,000 and
the soybean will net $10000. If the prices remain unchanged ,
McCoy will (barely) breakeven. But if the prices go down, the
corn and soybean crop will sustain losses of $35,000, & $5000
respectively.
•(a) Represent McCoy problem as a decision tree.
•(b) Which crop McCoy should plant
55
•Farmer McCoy can plant either corn or soybean. The
probabilities that the next harvest prices of these commodities
will go up, stay the same or go down are .25, .30, and .45
respectively. If the prices go up corn crop will net $30,000 and
the soybean will net $10000. If the prices remain unchanged ,
McCoy will (barely) breakeven. But if the prices go down, the
corn and soybean crop will sustain losses of $35,000, & $5000
respectively.
•(a) Represent McCoy problem as a decision tree.
•(b) Which crop McCoy should plant
55
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