Chapter 2 Supplement 2: Decision Analysis

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Chapter 2 Supplement 2 Decision Analysis

• Quantitative decision-making techniques
• for situations where uncertainty exists

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Decision Making

• States of nature
• Events that may occur in the future
• Decision maker is uncertain which state of nature
  will occur
• Decision maker has no control over the states of
  nature

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Decision Making

• Example Two possible states of nature
• Today it will rain OR Today it will not
  rain
• We are uncertain which state of nature will
  occur
• We have no control over the state of nature

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Payoff Table

• A method of organizing illustrating the payoffs
  from different decisions given various states of
  nature
• A payoff is the outcome (benefit or loss) of the
  decision

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Payoff Table

• States Of Nature
• Decision RAIN NO RAIN
• UMBRELLA stay dry stay dry
• NO UMBRELLA get wet stay dry

Two states RAIN or NO RAIN One decision
choose UMBRELLA or NO UMBRELLA Possible
outcomes stay dry or get wet
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Payoff Table

• States Of Nature
• Decision a b
• 1 Payoff 1a Payoff 1b
• 2 Payoff 2a Payoff 2b

Two states a and b One decision choose 1
or 2 Four possible outcomes Payoff 1a, 1b, 2a,
2b
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Payoff Table

• State Of Nature Projector..
• Decision Works Is Broken
• no backup OK cancel class
• have backup OK OK

Two states Projector Works or Projector
Broken One decision choose no backup or have
backup Possible outcomes OK or cancel class
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Payoff Table Single Coin Toss

• States Of Nature
• Decision heads tails
• choose heads win lose
• choose tails lose win

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Payoff Table Triple Coin Toss
Eight States Of Nature
Decision
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Payoff Table Snowboarding?
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Payoff Table Education
http//www.census.gov/
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Payoff Table Education

• Average Salary is not accurate enough as a
• predictor, need to factor additional
• states of nature into the decision process.
• There are many, lets pick two
• Good Economy, Growing Educational Demand
• Bad Economy, No Educational Demand

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Payoff Table Education

• Lets also simplify the decisions to be made to
  one
• of three
• Go on to obtain MBA
• Status quo, complete bachelors degree
• Drop out of school now
• and then look at several possible decision
  schemes.

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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
Go on to MBA 2,200,000 800,000 Maintain
status quo 1,800,000 1,000,000 complete
graduation Drop out now 1,000,000 900,000
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Decision Making Criteria Under Uncertainty

• Maximax criterion
• Choose decision with the maximum of the maximum
  payoffs
• Maximin criterion
• Choose decision with the maximum of the minimum
  payoffs
• Minimax regret criterion
• Choose decision with the minimum of the maximum
  regrets for each alternative

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Decision Making Criteria Under Uncertainty

• Hurwicz criterion
• Choose decision in which decision payoffs are
  weighted by a coefficient of optimism, ?
• Coefficient of optimism (?) is a measure of a
  decision makers optimism, from 0 (completely
  pessimistic) to 1 (completely optimistic)
• Equal likelihood (La Place) criterion
• Choose decision in which each state of nature is
  weighted equally

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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
MBA 2,200,000 800,000 Maintain status
quo 1,800,000 1,000,000 Drop out
now 1,000,000 900,000
Maximax Solution MBA 2,200,000 ?
Maximum Status quo 1,800,000 Drop out
1,000,000 Decision go for MBA
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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
MBA 2,200,000 800,000 Maintain status
quo 1,800,000 1,000,000 Drop out
now 1,000,000 900,000
Maximin Solution MBA 800,000 Status
quo 1,000,000 ? Maximum Drop out now
900,000 Decision Status quo, complete college
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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
MBA 2,200,000 800,000 Maintain status
quo 1,800,000 1,000,000 Drop out
now 1,000,000 900,000
Minimax Regret Solution 2.2M - 2.2M 0
1M-800K 200K 2.2M - 1.8M 400K
1M-1M 0 2.2M - 1M 1.2M 1M -
900K 100K
MBA 200,000 ? Minimum Status quo
400,000 Drop out now 1,200,000 Decision go
for MBA
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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
MBA 2,200,000 800,000 Maintain status
quo 1,800,000 1,000,000 Drop out
now 1,000,000 900,000
Hurwicz Criteria Coefficient of optimism ?
0.3 1 - ? 0.7 MBA 2.2M(0.3)
800,000(0.7) 1,220,000 Status quo
1.8M(0.3) 1M(0.7) 1,240,000 ? Maximum Drop
out 1M(0.3) 900,000(0.7)
930,000 Decision Status quo, complete college
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Decision Making with Probabilities

• Risk involves assigning probabilities to states
  of nature
• Expected value is a weighted average of decision
  outcomes in which each future state of nature is
  assigned a probability of occurrence

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Expected Value
where
xi outcome i p(xi) probability of outcome i
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Expected Value Example Coin Toss

• Tops a coin, two outcomes
• heads probability 0.5 x1 1.00
• tails probability 0.5 x2 0

p(x1) 1 p(x2)0
0.5 1 0.50 0.50
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Expected Value
100 chance of 10 chance of 1 chance of 0.1
chance of
0.01
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Expected Value Examples
EV (lottery) 50 investment EV (slot machine)
95 investment EV (savings account) 102
investment EV (cert of deposit) 105
investment EV (stock market) 110 investment
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Expected Value 10 investment-per-week
EV (lottery) 50 investment 10/week loses
2,600 / ten years EV (stock market) 110
investment 10/week gains 3,916 / ten years EV
Difference of 6,516
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Education Plan Payoff Table Effect on Lifetime
Earnings
STATES OF NATURE Good Economy Poor
Economy DECISION Growing Educational Demand No
Educational Demand
MBA 2,200,000 800,000 Maintain status
quo 1,800,000 1,000,000 Drop out
now 1,000,000 900,000
Expected Value p(good) 0.70 p(poor)
0.30 EV(MBA) 2.2M(0.7)
800K(0.3) 1,780,000 ? Maximum EV(status quo)
1.8M(0.7) 1M(0.3) 1,560,000 EV(drop
out) 1,000K(0.7) 900K(0.3)
970,000 Decision MBA
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Decision Analysis

• Weve dealt with states of nature, and
  probabilities of outcomes
• What about situations that are far more complex?
  Where there are more steps in a situation
  analysis?

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Sequential Decision Trees

• A graphical method for analyzing decision
  situations that require a sequence of decisions
  over time
• Decision tree consists of
• Square nodes - indicating decision points
• Circles nodes - indicating states of nature
• Arcs - connecting nodes

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Simple Decision Tree
OUTCOME
DECISION POINT
ARCS CONNECTING NODES
OUTCOME
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Simple Decision Tree
STATE or OUTCOME A
probability ofoutcome A
DECISION POINT
probability ofoutcome B
STATE or OUTCOME B
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Sequential Decision Tree
C
A
DECISION POINT
D
B
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Sequential Decision Tree Education Decisions
yes
MBA
MBA?
yes
Stay in school?
BS/BA
no
no
HS diploma
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Sequential Decision Tree
Decision needed Need to get to class, which
vehicle to drive?States of nature traffic or
no traffic
STATES OF NATURE Traffic No Traffic driving
time driving time
Drive F250 to school 40 minutes
30 minutes Drive 986 to school
35 minutes 25
minutes
35
Sequential Decision Tree
traffic
35 mins
P0.1
986
P0.9
25 mins
no traffic
What to drive?
40 mins
traffic
B
P0.1
F250
P0.9
30 mins
no traffic
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Sequential Decision Tree
35 mins
traffic
P0.1
986
EV986
P0.9
25 mins
no traffic
What to drive?
40 mins
traffic
B
P0.1
F250
EVF250
P0.9
30 mins
no traffic
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Sequential Decision Tree
traffic
35 mins
P0.1
EV986 0.135 0.925EV986 26 minutes
986
P0.9
25 mins
no traffic
What to drive?
40 mins
traffic
B
P0.1
EVF250 0.140 0.930EV250 31 minutes
F250
P0.9
30 mins
no traffic
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Sequential Decision Tree
Additional states of nature temperature warm or
cold
STATES OF NATURE Cold Warm lt60o gt60o
F250 starting time 5
minutes zero 986 starting time
zero zero
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Sequential Decision Tree
traffic
35 mins
P0.1
986
P0.9
25 mins
no traffic
What to drive?
0
gt60o
P0.5
F250
temp?
P0.5
5 minsto start
lt60o
40
Sequential Decision Tree
traffic
35 mins
P0.1
EV986 0.135 0.925EV986 26 minutes
986
P0.9
25 mins
no traffic
What to drive?
0
gt60o
P0.5
F250
temp?
P0.5
5 minsto start
lt60o
EVF250 0.550.1400.930 0.50.1400.930
EVF250 33.5 minutes