Decision Theory
Decision theory provides a rational way of choosing the best alternative. Every decision-
making situation involve several alternative actions. These alternative actions have their own
corresponding payoff. Payoff refers to the return of investment or the final outcome of a certain
decision. However, most of the time the decision maker does not know which alternative will be
the best for different state of nature. A state of nature is an occurrence over which a decision
maker has no control.
There are three types of decision-making criteria under uncertainty:
1. Maximax Criterion/Optimistic Approach
2. Maximin Criterion/Conservative Approach
3. Minimax Regret Criterion
Maximax Criterion (Optimistic Approach)
It is the type of approach that chooses the alternative that is the “best of the best”. This
approach is optimistic as it is a “go for it” strategy that has high expectations. It yields the largest
maximum payoff among the alternatives.
Maximin Criterion (Conservative Approach)
This alternative chooses the “best of the worst”. It takes account to the only worst possible
outcome for each alternative. It maximizes the minimum payoffs. It is very conservative approach
that it takes a pessimistic view on the various states of nature.
Minimax Regret Criterion
It chooses the alternative with the best “worst regret”. This approach involves the
construction of an opportunity loss or regret matrix before choosing the decision with the smallest
maximum regret.
, Example: A farmer in Region II must decide which crop to plant next year on his land: corn,
peanut, or soybeans. The return form each crop will be determined by whether a new trade bill
passes the Senate. The profit of the farmer will realize from each crop given the two possible
results on the trade bill is shown in the following payoff table.
Trade Bill
Crop Pass Fail
Corn 2,000,000 700,000
Peanuts 1,100,000 500,000
Soybeans 1,400,000 1,200,000
Determine the best alternative for each decision rule.
Solution:
Maximax Criterion
Step 1: Select the column with the maximum payoff.
Trade Bill
Crop Pass Fail
Corn 2,000,000 700,000
Peanuts 1,100,000 500,000
Soybeans 1,400,000 1,200,000
Step 2: Identify the highest maximum payoff.
Trade Bill
Crop Pass
Corn 2,000,000 maximum payoff
Peanuts 1,100,000
Soybeans 1,400,000
Answer: The decision is to plant corn that will result in a maximum payoff of P2,000,000.
Decision theory provides a rational way of choosing the best alternative. Every decision-
making situation involve several alternative actions. These alternative actions have their own
corresponding payoff. Payoff refers to the return of investment or the final outcome of a certain
decision. However, most of the time the decision maker does not know which alternative will be
the best for different state of nature. A state of nature is an occurrence over which a decision
maker has no control.
There are three types of decision-making criteria under uncertainty:
1. Maximax Criterion/Optimistic Approach
2. Maximin Criterion/Conservative Approach
3. Minimax Regret Criterion
Maximax Criterion (Optimistic Approach)
It is the type of approach that chooses the alternative that is the “best of the best”. This
approach is optimistic as it is a “go for it” strategy that has high expectations. It yields the largest
maximum payoff among the alternatives.
Maximin Criterion (Conservative Approach)
This alternative chooses the “best of the worst”. It takes account to the only worst possible
outcome for each alternative. It maximizes the minimum payoffs. It is very conservative approach
that it takes a pessimistic view on the various states of nature.
Minimax Regret Criterion
It chooses the alternative with the best “worst regret”. This approach involves the
construction of an opportunity loss or regret matrix before choosing the decision with the smallest
maximum regret.
, Example: A farmer in Region II must decide which crop to plant next year on his land: corn,
peanut, or soybeans. The return form each crop will be determined by whether a new trade bill
passes the Senate. The profit of the farmer will realize from each crop given the two possible
results on the trade bill is shown in the following payoff table.
Trade Bill
Crop Pass Fail
Corn 2,000,000 700,000
Peanuts 1,100,000 500,000
Soybeans 1,400,000 1,200,000
Determine the best alternative for each decision rule.
Solution:
Maximax Criterion
Step 1: Select the column with the maximum payoff.
Trade Bill
Crop Pass Fail
Corn 2,000,000 700,000
Peanuts 1,100,000 500,000
Soybeans 1,400,000 1,200,000
Step 2: Identify the highest maximum payoff.
Trade Bill
Crop Pass
Corn 2,000,000 maximum payoff
Peanuts 1,100,000
Soybeans 1,400,000
Answer: The decision is to plant corn that will result in a maximum payoff of P2,000,000.
