Lecture 3 Decision Analysis

Topics: Decision theory, Decision making, Game theory Pages: 54 (2433 words) Published: December 5, 2014
Decision Analysis

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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