Overview

Decision Trees Basic analytical tool of decision making Non-strategic decisions Strategic decisions

Decision rules follow from decision trees The concept of economic profit

Decisions Degree of interdependence

Non-strategic Direct consequences of your decision depend only upon your own behavior, not that of others

Strategic Agents’ actions interact to determine direct consequences for all

Uncertainty Low Linkages between actions and consequences are well

understood and completely specified High Linkages are partially understood and/or incompletely

specified

Types of Decisions

Degree of Uncertainty

Low High

Deg

ree

of I

nter

depe

nden

ce

with

oth

ers’

act

ions

High

Low

Market entry

Extreme sports

What to wear

What to have for lunch

How hard to study

Whether to do an MBA

Which MBA

What to bid

Decision Trees

The basic tool for decision making is a decision tree

Idea: a traveller comes to a fork in the road. She must make a decision whether to go right or left.

R

L

Example (non-strategic under certainty)

= Decision Node: indicates a point at which an action must be taken(one path for each possible action)

CBD $120,000

$150,000Brunswickopen a restaurant

don’t $0

Entry decision

Location decision

Chang’s Dilemma in 2003

Sarah Chang is the owner of a small electronics company. There is a proposal for the provision of an electronic timing system for the 2004 Olympic Games. For several years, Chang’s company has been developing a new microprocessor, a critical component in a timing system that would be superior to any product currently on the market.

Progress has been slow and Chang is unsure about whether the new product will be developed on time. If the R&D succeeds, then there is an excellent chance her company will win the $1m Olympic contract; awarded solely on the basis of quality. If it does not succeed, they might still win the contract with their original, but inferior, system for which there are closer substitutes.

The costs involved in continuing R&D are $200,000. Developing a proposal itself will cost Chang’s company $50,000. Finally, the costs of producing the product – should they win the contract – will be $150,000.

Should Chang continue R&D or not?

Framing the Decision: Step I Chang’s decision is between two alternatives

– to continue R&D or to abandon the project

Abandon

Continue

Perhaps make proposal with inferior technology at an additional cost of $50,000

Take risk on developing the new technology at an additional cost of $200,000 and reconsider proposal

Step II

Abandon

Continue

Not

Proposal

$0

Expend $50,000 and perhaps win

Uncertainty in a decision tree

Chang must assess the probability of success Objective based upon data or specific knowledge Subjective based upon experience & judgement

Suppose the probability of winning the contract with the old product is only 5% = 0.05

This implies probability of losing is 95%

= Random Event Node: point at which “Nature” takes an action of her own (one path for each possible outcome)

Step III

Abandon

Continue

Not

Proposal

$0

Win

Lose

0.05

0.95

$800,000

-$50,000

Abandon

Continue

Not

Proposal

$0

Win

Lose

0.05

0.95

-$50,000

Succeed

Fail

0.5

0.5

$800,000

Expend $50,000 and perhaps win

Expend $50,000 and have a good chance of winning

Step IV

Step V

Abandon

Continue

$0

W

L

0.05

0.95

-$50,000

Succeed

Fail

0.5

0.5

$800,000

No

Prop

-$200,000

W

L

0.9

0.1

-$250,000

$600,000

-$200,000

W

L

0.05

0.95

-$250,000

$600,000

No

Prop

No

Prop

Optimal decision plan

While we built the tree by adding branches …the way to “solve” it is to start at the end and

‘roll back.’

Looking forward and working backwards is a key skill in economic decision-making

Example (non-strategic under certainty)

First, solve a node furthest to the right Decision node: Pick the best choice Nature node: Calculate the average value

Solve next node to the left Continue …

CBD $120,000

$150,000Brunswickopen a restaurant

don’t $0

Solving at a node with uncertainty: Expected value

Chang wants to know, is R&D a risk worth taking? Easy to solve, so long as Chang is risk-neutral;

Risk-neutral agents prefer decisions with highest average payoff Good assumption when agent is a firm, poor for individuals

(investors can diversify their own portfolios)

Example: Flip a coin, Heads you get $2.10 Tails you lose $1.00

1000 flips: roughly 500 heads, 500 tails an average of ? per flip.

Expected value: = (Probability of heads)(Payoff if heads) + (Prob of tails)(Payoff if tails)

= ½ x 2.1 + ½ x (-1.00)= ½ x (2.1 – 1.00)= $ 0.55

Solving the Tree

Abandon

Continue

Not

Proposal

$0

Win

Lose

0.05

0.95

$800,000

-$50,000

?

Expected value =

0.05 ($800,000) + 0.95 (-$50,000)

= - $7,500

Solving the Tree

Abandon

Continue

Not

Proposal

$0

-$7,500

?

Choose the branch with the best payoff

Solving the Tree

Abandon

Continue

Succeed

Fail

0.5

0.5

$0

Not

Proposal

-$200,000

Win

Lose

0.9

0.1-$250,000

$600,000

Not

Proposal

-$200,000

Win

Lose

0.05

0.95-$250,000

$600,000

Solving the Tree

Abandon

Continue

Succeed

Fail

0.5

0.5

$0

Not

Proposal

-$200,000

Win

Lose

0.9

0.1-$250,000

$600,000

Not

Proposal

-$200,000

-$207,500

Solving the Tree

Abandon

Continue

Succeed

Fail

0.5

0.5

$0

Not

Proposal

-$200,000

$515,000

-$200,000

Solving the Tree

Abandon

Continue

Succeed

Fail

0.5

0.5

$0

$515,000

-$200,000

Solving the Tree

Abandon

Continue

$0

$157,500

1. Never make proposal if don’t have newer technology

2. Choose to take risk and continue R&D

Indy’s ChoiceExample (from Dixit & Nalebuff): Indiana Jones in the climax of the movie Indiana Jones and the Last Crusade.

Indiana Jones, his father, and the Nazis have all converged at the site of the Holy Grail. The two Joneses refuse to help the Nazis reach the last step. So the Nazis shoot Indiana’s dad. Only the healing power of the Holy Grail can save the senior Dr. Jones from his mortal wound. Suitably motivated, Indiana leads the way to the Holy Grail. But there is one final challenge. He must choose between literally scores of chalices, only one of which is the cup of Christ. While the right cup brings eternal life, the wrong choice is fatal. The Nazi leader impatiently chooses a beautiful gold chalice, drinks the holy water, and dies from the sudden death that follows from the wrong choice. Indiana picks a wooden chalice, the cup of a carpenter. Exclaiming “There’s only one way to find out” he dips the chalice into the font and drinks what he hopes is the cup of life. Upon discovering that he has chosen wisely, Indiana brings the cup to his father and the water heals the mortal wound.

Framing the Decision What alternatives does Indy have?

Give drink to Snr

Drink himself

Framing the Decision Do you need more information?

Give drink to Snr

Drink himself

Right

Wrong

Jnr & Snr Live

Jnr & Snr Die

Right

Wrong

Jnr & Snr Live

Snr Dies but Jnr Lives

Uses of Decision Trees Decision Trees are used in situations that may be too

complex to think through in your mind

In Decision Analysis: used in situations where there is uncertainty, multiple decisions

In “Managerial Economics”: used in situations where The payoffs are not so obvious The alternative choices are not so obvious Several players have to make choices

Being systematic helps you to see though complexity and to remember all your alternative choices

Economic Cost = opportunity foregone

The true cost of one choice is giving up the benefits associated with your next-best choice

Example: What is the cost of doing an MBA? Besides the price, there is an opportunity cost =

what you would have earned, using the resource (your time) for another opportunity

Costs that do not change with your decision are irrelevant

Consider this situation

Mita runs petrol stations and express stores at several highway exits. Until recently, she didn’t sell any drinks. She brought in a new line of drinks, Fizzies, which have proved unpopular.

She has 10,000 Fizzies left. She thinks she can sell half of the remaining drinks for $1.00, but only 15% of the drinks at the standard price of $2.50. If she paid $0.30 per drink, how much should she charge? What about if she paid $1.05 per drink?

Mita cannot return unsold stock of Fizzies, but must throw the stock out.

Definition: Sunk CostA cost is considered sunk with respect to a specific decision if, no matter what you decide, that cost does not change

On a decision tree, a sunk cost appears on all leaves (payoffs)

sell at $2.50 $3750 - costMita sell at $1.00 $5000 - cost

Economic benefit of charging $1 rather than $2.5 is $1,250(cost is the same in all cases … it is sunk & irrelevant)

Definition: *** Economic Profit *** The economic profit of a decision is the cash you earn from one

decision, minus that from the best alternative decision

Decision tree: $ from best choice, minus $ from next best choice

sell at $2.50 $3750 - costMita sell at $1.00 $5000 - cost

Economic profit = $1,250