chapter 14 decision making

Chapter 14 Decision Making

Applying Probabilities to the Decision-Making Process in

the face of uncertainty.

In order to make the best decision, with the information available, the decision maker

utilizes certain decision strategies to evaluate the possible benefits and losses of each alternative.

When making a decision in the face of uncertainty, ask:

1) What are my possible Alternatives or Courses of Action?

2) How can the future affect each action?

What are my possible Alternatives or Courses of Action?

Before selecting a course of action, the decision maker must have at least two possible alternatives to evaluate before making his choice.

Example: I want to invest $1 million for 1 year. I narrow my choices to three alternatives

(actions):

Alternative 1: Invest in guaranteed income certificate paying 10%.

Alternative 2: Invest in a bond with a coupon value of 8%.

Alternative 3: Invest in a well-diversified portfolio of stocks.

The Alternatives (Actions) are under the decision maker’s control.

How can the future affect each alternative (action)?

Unless you’ve got a crystal ball

Future uncertainties may derail the most perfect of plans.

These future events are also referred to as States of Nature

Example: Economic conditions, foremost among which is interest rates.

Interest rates increase.

Interest rates stay the same.

Interest rates decrease.

To account for future uncertainties (events)

We assign probabilities to measure the likelihood of a future event

occurring.

Example: Probabilities

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

Future events (states of nature or outcomes), are out of the

decision maker’s control and often strictly a matter of

chance.

Yet, the impact of these events

Affect the payoffs/losses which determine the decision

making process.

Important Distinction!

The action (alternative) is under the decision maker’s control.

The event (state of nature) that ultimately occurs is strictly a matter of chance.

Associated with each alternative (action) and event (state of nature) is a

corresponding payoff or profit.

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

If I could predict the future with certainty,

I would choose the alternative with the highest payoff (profit).

Instead of focusing on profits, I could look at the Opportunity Loss associated with each

combination of an alternative and the economic

condition affecting that alternative’s profitability.

Opportunity Loss

The difference between the profit I made on the alternative I chose and the profit I could have made had the best decision been made.

OPPORTUNITY LOSS TABLE Interest rates GIC Bond Stocks Increase $50,000 $200,000 0 Stay same 0 20,000 10,000 Decrease 80,000 0 140,000

NOTE:Since Opportunity Loss is the difference

between two decisions, it can not be expressed as a negative number.

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

If I could predict the future with certainty,

I would choose the alternative (action) with the highest payoff or lowest loss.

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

OPPORTUNITY LOSS TABLE Interest rates GIC Bond Stocks Increase $50,000 $200,000 0 Stay same 0 20,000 10,000 Decrease 80,000 0 140,000

In many decision problems, it is impossible to assign Empirical probabilities to the

economic events, or states of nature, that affect profits and losses. In many cases,

probabilities are assigned Subjectively.

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

Using probabilities, we calculate the Expected Monetary Value for

each alternative or action.

Expected Monetary Value (EMV)PAYOFF TABLE

Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

EXPECTED MONETARY VALUE EMV (GIC) = .2(100,000) + .5(100,000) + .3(100,000) = $100,000 EMV (Bond) = .2(-50,000) + .5(80,000) + .3(180,000) = $84,000 EMV (Stocks) = .2(150,000) + .5(90,000) + .3(40,000) = $87,000

To maximize profits, choose the Alternative with the highest EMV.

EXPECTED MONETARY VALUE EMV (GIC) = .2(100,000) + .5(100,000) + .3(100,000) = $100,000 EMV (Bond) = .2(-50,000) + .5(80,000) + .3(180,000) = $84,000 EMV (Stocks) = .2(150,000) + .5(90,000) + .3(40,000) = $87,000

What does the EMV represent?

If the investment is made a large number of times (infinite)

with bonds,* 20% of the investments will result in a $50,000

loss,* 50% will result in an $80,000 profit, and* 30 % will result in $180,000 profit.

The average of all these investments is the EMV of $84,000.

Expected Opportunity Loss Decision (EOL)

Expected Opportunity Loss (EOL)OPPORTUNITY LOSS TABLE

Interest rates GIC Bond Stocks Increase $50,000 $200,000 0 Stay same 0 20,000 10,000 Decrease 80,000 0 140,000

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

EXPECTED OPPORTUNITY LOSS (EOL) DECISION EOL (GIC) = .2(50,000) + .5(0) + .3(80,000) = $34,000 EOL (Bond) = .2(200,000) + .5(20,000) + .3(0) = $50,000 EOL (Stocks) = .2(0) + .5(10,000) + .3(140,000) = $47,000

To minimize losses, choose the Alternative with the lowest EOL.

EXPECTED OPPORTUNITY LOSS (EOL) DECISION EOL (GIC) = .2(50,000) + .5(0) + .3(80,000) = $34,000 EOL (Bond) = .2(200,000) + .5(20,000) + .3(0) = $50,000 EOL (Stocks) = .2(0) + .5(10,000) + .3(140,000) = $47,000

Example

A vendor at a baseball game must determine whether to sell ice cream or soft drinks at today’s game. The vendor believes that the profit made will depend on the weather.

Based on past experience at this time of year, the vendor estimates the

probability of warm weather as 60%.

ACTION Event Sell Soft Drinks ($) Sell Ice Cream ($)

Cool Weather 50 30 Warm Weather 60 90

1) Compute the EMV for selling soft drinks and selling ice cream.

2) Compute the EOL for selling soft drinks and ice cream.

3) Based on the previous results, which should the vendor sell, ice cream or soft drinks? Why?

ACTION Event Sell Soft Drinks ($) Sell Ice Cream ($)

Cool Weather 50 30 Warm Weather 60 90

EMV

EMV (soft drinks) = .4(50) + .6(60) = 20 + 36 = $56

EMV (ice cream) = .4(30) + .6(90) = 12 + 54 = $66

Sell ice cream

Stay tuned

The Value of Additional Information

If we knew in advance which future event or state of nature would occur, we would capitalize on this knowledge and maximize our profits/minimize our losses.

But our “knowledge” of future events or states of nature is sometimes tenuous at best.

Leaving us to ask ourselves, “Am I making the best decision?”

To determine which course of action (alternative)

to select, we assign probabilities to the likelihood of each future event occurring.

Probabilities are assigned based on :

• past data,

• the subjective opinion of the decision maker,

• Or knowledge about the probability distribution that the event may follow.

Better information makes better decisions.

But what are you willing to pay?

Data is costly to acquire:

* Money & time

• Cognitive energy

• Staff effort

• Opportunity costs of failing to do other things with the money or time.

Goal is to gather data as long as:

the MARGINAL COST is NO MORE than the MARGINAL BENEFITS of the additional data.

At some point, data gathering must stop and the decision must be made.

The Value of Additional Information

Expected Payoff with Perfect Information (EPPI)

EPPI is the maximum price that a decision maker should be willing to pay for perfect information.

With perfect information,

I would know what to expect so I would select the optimum course of action for each future event.

Expected Payoff With Perfect Information (EPPI)

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

EPPI = .2(150,000) + .5(100,000) + .3(180,000) = $134,000

EXPECTED PROFIT UNDER CERTAINTY is the expected profit you could make if you have perfect information about WHICH event will occur.

EPPI is also known as Expected Profit under Certainty.

If the Expected Profit Under Certainty (EPPI) is the profit I expect to make if have perfect information

about which event will occur, how much should I be

willing to pay for this “perfect” information?

The $134,000 does NOT represent the MAXIMUM amount I’d be willing to pay for perfect information because I could have made an expected profit of EMV= $100,000 WITHOUT perfect information.

EPPI = .2(150,000) + .5(100,000) + .3(180,000) = $134,000

Expected Value of Perfect Information

EVPI = EPPI – EMV* = $134,000 - $100,000

= $34,000

If perfect information were available, the decision maker should be willing to pay up to $34,000 to acquire it.

Besides profits & losses, is there something else we should

consider?

Variability!

When comparing two or more actions, especially with vastly different means, evaluate the relative risk associated with each action.

Coefficient of Variation (CV)

Return to Risk Ratio (RRR)

Coefficient of Variation (CV)

Measures the relative size of the variation compared with the arithmetic mean (EMV).

CV = σ ÷ EMV

σ = √Σ (x- µ)2 · P (X)Where µ = EMV*

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

Interest rates Probabilities Increase .2 Stay same .5 Decrease .3

CV = σ ÷ EMV σ = √Σ (x- µ)2 · P (X)

Where µ = EMV*

EXPECTED MONETARY VALUE EMV (GIC) = .2(100,000) + .5(100,000) + .3(100,000) = $100,000 EMV (Bond) = .2(-50,000) + .5(80,000) + .3(180,000) = $84,000 EMV (Stocks) = .2(150,000) + .5(90,000) + .3(40,000) = $87,000

EMV* = $100,000

σstocks = √Σ (x- µ)2 · P (X)

= √(150,000 – 100,000) 2 (.2) + (90,000 – 100,000) 2 (.5) +

(40,000 – 100,000) 2 (.3)

= 40,373

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

EMV* = $100,000

σbonds = √Σ (x- µ)2 · P (X)

= √(-50,000 – 100,000) 2 (.2) + (80,000 – 100,000) 2 (.5) +

(180,000 – 100,000) 2 (.3)

= 81,363

PAYOFF TABLE Interest rates GIC Bond Stocks Increase $100,000 -$50,000 $150,000 Stay same $100,000 $80,000 $ 90,000 Decrease $100,000 $180,000 $ 40,000

Coefficient of Variation

CVstocks = (σ ÷ EMV) 100%= (40,373 ÷ 100,000) 100%= 40.4%

CVbonds = (σ ÷ EMV) 100%= (81,363 ÷ 100,000) 100%= 81.4%

Return-to-Risk Ratio (RRR)

RRR = EMV ÷ σ

RRR stocks = 100,000 ÷ 40,373 = 2.48

RRR bonds = 100,000 ÷ 81,363 = 1.23

Although Bonds & stocks have a comparable EMV, the

RRR for stocks is substantially higher than bonds & the

stocks’ CV much smaller than that of bonds.

EXPECTED MONETARY VALUE EMV (GIC) = .2(100,000) + .5(100,000) + .3(100,000) = $100,000 EMV (Bond) = .2(-50,000) + .5(80,000) + .3(180,000) = $84,000 EMV (Stocks) = .2(150,000) + .5(90,000) + .3(40,000) = $87,000

RRR stocks = 100,000 ÷ 40,373 = 2.48

RRR bonds = 100,000 ÷ 81,363 = 1.23

Homework

A baker must decide how many specialty cakes to bake each morning. From past experience, she knows that the daily demand for cakes ranges from 0 to 3. Each cake costs $3.00 to produce and sells for $8.00, and any unsold cakes are thrown in the garbage at the end of the day.

Set up a payoff table to help the baker decide how many cakes to bake.

Payoff Table

Produce

Demand Bakeo Bake1 Bake2 Bake3

Sello 0 -3.00 -6.00 -9.00

Sell1 0 5.00 2.00 -1.00

Sell2 0 5.00 10.00 7.00

Sell3 0 5.00 10.00 15.00

Opportunity Loss Table

Produce

Demand Bakeo Bake1 Bake2 Bake3

Sello 0 3.00 6.00 9.00

Sell1 5.00 0 3.00 6.00

Sell2 10.00 5.00 0 3.00

Sell3 15.00 10.00 5.00 0

Assuming probability of each event is equal: Sell = .25

EMV(0) = $ 0EMV(1) = .25(-3) + .25(5) + .25(5) + .25(5)= $3.00EMV(2) = .25(-6) + .25(2) +.25(10) + .25(10)= $4.00EMV(3) = .25(-9) + .25(-1) +.25(7) + .25(15)= $3.00EMV* decision is to bake 2 cakes.

Assuming probability of each event is equal: Sell = .25

EOL(0) = .25(0) + .25(5) + .25(10) =.25(15)

= $7.50

EOL(1) = .25(3) + .25(0) + .25(5) =.25(10)

= $4.50

EOL(2) = .25(6) + .25(3) + .25(0) =.25(5)

= $3.50

EOL(3) = .25(9) + .25(6) + .25(3) =.25(0)

= $4.50

EOL* decision is to bake 2 cakes.

EVPI = EPPI – EMV*

EPPI= .25(-3) + .25(5) + .25(10) + .25(15)

= $6.75

EMV = $4.00

EVPI = $6.75 – 4.00 = $2.75

Homework

The manager of a large shopping center in Buffalo is in the process of deciding on the type of snow clearing service to hire for his parking lot. Two services are available. The White Christmas Company will clear all snowfalls for a flat fee of $40,000 for the entire winter season. The Weplowmen Company charges $18,000 for each snowfall it clears.

Set up the payoff table to help the manager decide, assuming that the number of snowfalls per winter

season ranges from 0 to 4.

Payoff Table

Demand Flat FeePay per snowfall

# of Snowo

-40,000 0

# of Snow1

-40,000 -18,000

# of Snow2

-40,000 -36,000

# of Snow3

-40,000 -54,000

# of Snow4

-40,000 -72,000

Using subjective assessments, the manager has assigned the following probabilities to the number of snowfalls. Determine

the optimal decision.

• p(0) = .05

• p(1) = .15

• p(2) = .30

• p(3) = .40

• p(4) = .10

EMV (flat fee) = - $40,000EMV (pay per snowfall) = .5(0) + .15(-18,000) + .3(-36,000) + .4( -54,000) + .1(-72,000)

= -$42,000EMV* is flat fee

Hopefully, something hit home