# Lecture 3 Decision Analysis

**Topics:**Decision theory, Decision making, Game theory

**Pages:**54 (2433 words)

**Published:**December 5, 2014

Example

Consider the following problem with three decision

alternatives and three states of nature with the following

payoff table representing profits:

States of Nature

s1

s2

s3

d1

4

4

Decisions d2

0

3

d3

1

5

Which decision do you choose?

-2

-1

-3

Problem Formulation

• A decision problem is characterized by decision

alternatives, states of nature, and resulting payoffs.

• The decision alternatives are the different possible

strategies the decision maker can employ.

• The states of nature refer to future events, not under

the control of the decision maker, which may occur.

States of nature should be defined so that they are

mutually exclusive and collectively exhaustive.

Payoff Tables

• The consequence resulting from a specific combination

of a decision alternative and a state of nature is a payoff. • A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table.

• Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate measure.

Decision Making without Probabilities

• Three commonly used criteria for decision making

when probability information regarding the likelihood

of the states of nature is unavailable are:

– the optimistic approach

– the conservative approach

– the minimax regret approach.

Optimistic Approach

• The optimistic approach would be used by an

optimistic decision maker.

• The decision with the largest possible payoff is

chosen.

• If the payoff table was in terms of costs, the decision

with the lowest cost would be chosen.

Example

Consider the following problem with three decision

alternatives and three states of nature with the following

payoff table representing profits:

States of Nature

s1

s2

s3

d1

Decisions d2

d3

4

0

1

4

3

5

-2

-1

-3

Example: Optimistic Approach

An optimistic decision maker would use the

optimistic (maximax) approach. We choose the decision

that has the largest single value in the payoff table.

Maximax

decision

Maximum

Decision

Payoff

d1

4

d2

3

d3

5

Maximax

payoff

Conservative Approach

• The conservative approach would be used by a

conservative decision maker.

• For each decision the minimum payoff is listed and

then the decision corresponding to the maximum of

these minimum payoffs is selected. (Hence, the

minimum possible payoff is maximized.)

• If the payoff was in terms of costs, the maximum costs

would be determined for each decision and then the

decision corresponding to the minimum of these

maximum costs is selected. (Hence, the maximum

possible cost is minimized.)

Example

Consider the following problem with three decision

alternatives and three states of nature with the following

payoff table representing profits:

States of Nature

s1

s2

s3

d1

Decisions d2

d3

4

0

1

4

3

5

-2

-1

-3

Example: Conservative Approach

A conservative decision maker would use the

conservative (maximin) approach. List the minimum

payoff for each decision. Choose the decision with the

maximum of these minimum payoffs.

Maximin

decision

Minimum

Decision

Payoff

d1

-2

d2

-1

d3

-3

Maximin

payoff

Minimax Regret Approach

• The minimax regret approach requires the

construction of a regret or opportunity loss table.

• Regret: for each state of nature (column), regret for a

decision is the difference between that payoff and the

largest one.

– Regret is with respect to decisions, not states of

nature.

• Minimax regret:

– Find maximum regret for each decision.

– Choose decision with the smallest maximum regret

Example

Consider the following problem with three decision

alternatives and three states of nature with the following

payoff table representing profits:

States of Nature

s1

s2

s3

d1

Decisions d2

d3

4

0

1

4

3

5

-2

-1

-3

Example: Minimax Regret

Approach

For the minimax regret...

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