Performance Management · Dealing with risk and uncertainty in decision-making

Maximin, Maximax and Minimax Regret Decision Rules in ACCA PM

Updated 11 October 2026 · Fact-checked

Maximin, maximax and minimax regret are decision rules for choosing between options when you cannot assign probabilities. Build a pay-off table. Maximin picks the option with the best worst outcome. Maximax picks the best best outcome. Minimax regret picks the option whose largest regret, the gap from the best choice in each state, is smallest.

Understand Decision Rules: Maximin, Maximax and Minimax Regret

Sometimes a manager must choose between options but cannot put probabilities on what may happen. This is uncertainty. A pay-off table helps. Each row is an option. Each column is a possible future, called a state of nature or outcome. Each cell shows the profit (or cost) if you pick that option and that future happens.

The decision rules turn the table into one choice. They match the attitude of the decision-maker. They do not use probabilities, so they do not find the 'average' result.

Maximin is the pessimist's rule. For each option, find the worst outcome. Then choose the option whose worst outcome is the best. It protects you against the downside.

Maximax is the optimist's rule. For each option, find the best outcome. Then choose the option with the highest of these. It chases the biggest possible gain.

Minimax regret is for a decision-maker who hates looking back and wishing they had chosen differently. Regret is the profit you lose by not choosing the best option for the state that actually happens. You build a regret table, find the largest regret for each option, and choose the option with the smallest largest regret. The three rules often give three different answers. That is normal.

Key rules to remember

Maximin (profits): Choose the option with the highest minimum pay-off; Pessimistic, risk-averse. Find the lowest figure in each row, then pick the largest of those.
Maximax (profits): Choose the option with the highest maximum pay-off; Optimistic, risk-seeking. Find the highest figure in each row, then pick the largest of those.
Regret for a cell: Regret = best pay-off in that state − pay-off of the option in that state; Work down each column. The best option in a state has regret of zero. For costs, regret = option's cost − lowest cost in that state.
Minimax regret: Choose the option with the lowest maximum regret; Find the largest regret in each row of the regret table, then pick the smallest of those.
Rules for costs: Minimax: choose the lowest of the maximum costs. Minimin: choose the lowest of the minimum costs; When the table shows costs, the logic flips. Pessimist looks at the highest cost for each option and wants the smallest of those.

How to solve Decision Rules: Maximin, Maximax and Minimax Regret questions

Use this method for any pay-off table question. Check first whether the figures are profits or costs, because that decides which way you compare.

1Read the table. Note whether the figures are profits or costs, and which are options (rows) and which are states (columns).
2For maximin (profits): write the lowest figure in each row. Pick the option with the highest of these.
3For maximax (profits): write the highest figure in each row. Pick the option with the highest of these.
4For regret: find the best figure in each column (highest for profits, lowest for costs).
5Build the regret table. In each cell, subtract the option's figure from the column's best figure (profits), or the reverse (costs). Every column must contain at least one zero.
6Write the largest regret in each row. Pick the option with the smallest of these. This is the minimax regret choice.
7State each answer clearly with the option name and the figure that decided it.
8If asked to comment, link each rule to the decision-maker's attitude to risk and note that none of the rules uses probabilities.

Quickest way: Column-best, then row-worst

When to use it: Use in Section A or an OT case where you only need the chosen option and have about three minutes.

Circle the best figure in each column first. You need these for regret.
Scan each row once: note the lowest and highest figure beside the row.
Maximin and maximax come straight from those notes.
For regret, work out each cell mentally as best in column minus the cell. Only keep the largest per row.
Check that the winning option under each rule is a different one only if the numbers say so. Do not force different answers.

Common mistakes in Decision Rules: Maximin, Maximax and Minimax Regret

Calculating regret across the row instead of down the column.
Students compare an option with its own other outcomes.
Fix: Regret is always measured within one state. Take the best figure in the column and compare each option against it.
Choosing the largest regret instead of the smallest of the maximum regrets.
The word 'maximum' is confused with the choice.
Fix: Find the maximum regret for each option, then choose the option where that maximum is lowest.
Applying profit rules to a cost table.
Students follow the method on autopilot.
Fix: Check the label first. For costs, the best figure in a column is the lowest, and the pessimist looks at the highest cost.
Choosing the pay-off figure rather than the option.
The calculation ends on a number, so students quote it.
Fix: The question asks which option to choose. Name the option and give the figure as support.
Using probabilities or expected values in these rules.
Students mix this topic with expected value questions.
Fix: If no probabilities are given, use only the pay-off figures. Expected value is a different technique.
Subtracting in the wrong direction and getting negative regret.
Rushing and reversing the subtraction.
Fix: Regret can never be negative. If you get a negative, reverse the subtraction.

Worked examples

Example 1

A company can launch Product A, B or C. Profits ($000) depend on demand: Good, Fair or Poor. A: 80, 50, 10. B: 60, 55, 30. C: 100, 40, −20. No probabilities are available. Which product is chosen under maximin, maximax and minimax regret?

Show the solution

Maximin: lowest in each row is A = 10, B = 30, C = −20. The highest of these is 30, so choose B.
Maximax: highest in each row is A = 80, B = 60, C = 100. The highest of these is 100, so choose C.
Best in each column: Good = 100, Fair = 55, Poor = 30.
Regret for A: 100 − 80 = 20; 55 − 50 = 5; 30 − 10 = 20. Maximum regret = 20.
Regret for B: 100 − 60 = 40; 55 − 55 = 0; 30 − 30 = 0. Maximum regret = 40.
Regret for C: 100 − 100 = 0; 55 − 40 = 15; 30 − (−20) = 50. Maximum regret = 50.
Smallest maximum regret is 20, so choose A.

Answer: Maximin: Product B ($30,000 worst case). Maximax: Product C ($100,000 best case). Minimax regret: Product A (maximum regret $20,000).

Example 2

A firm can buy a component from supplier X, Y or Z. Total annual cost ($000) depends on demand: High, Medium or Low. X: 120, 100, 90. Y: 110, 105, 115. Z: 130, 95, 85. Which supplier is chosen using the minimax (cost) rule and the minimax regret rule?

Show the solution

The figures are costs, so lower is better.
Minimax cost: highest cost for each supplier is X = 120, Y = 115, Z = 130. The lowest of these is 115, so choose Y.
Best (lowest) in each column: High = 110, Medium = 95, Low = 85.
Regret for X: 120 − 110 = 10; 100 − 95 = 5; 90 − 85 = 5. Maximum regret = 10.
Regret for Y: 110 − 110 = 0; 105 − 95 = 10; 115 − 85 = 30. Maximum regret = 30.
Regret for Z: 130 − 110 = 20; 95 − 95 = 0; 85 − 85 = 0. Maximum regret = 20.
The smallest maximum regret is 10, so choose X.

Answer: Minimax cost rule: supplier Y (worst-case cost $115,000). Minimax regret: supplier X (maximum regret $10,000).

Exam tips

Look at the units and the label. A cost table reverses every comparison, and this is the most common trap in OT questions.
Show the regret table in constructed-response answers. Markers give credit for the workings even if you slip on the final choice.
Link each rule to an attitude: maximin is pessimistic, maximax is optimistic, minimax regret avoids hindsight. Many written parts ask for this.
Mention the limitations: the rules ignore probabilities and use only one outcome per option (or the gap to the best), so they ignore the rest of the data.
Objective test questions are all or nothing. Re-check the column-best figures before you select an answer.

Practice questions from Dealing with risk and uncertainty in decision-making

Decision Rules: Maximin, Maximax and Minimax Regret in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Decision Rules: Maximin, Maximax and Minimax Regret: frequently asked questions

What is the difference between maximin and maximax?

Maximin looks at the worst outcome of each option and picks the best of these, so it suits a cautious decision-maker. Maximax looks at the best outcome of each option and picks the highest, so it suits an optimist. They often recommend different options.

How do I calculate a minimax regret table?

In each column, find the best pay-off. For each cell, subtract the option's pay-off from that best figure (for profits). The best option in each column gets zero. Then take the largest regret in each row and choose the smallest of these.

Do these decision rules use probabilities?

No. They are used when probabilities cannot be estimated. If probabilities are given, the question usually wants expected values, though the examiner may ask you to compare the two approaches.

Can the three rules give the same answer?

Yes. If one option is clearly better in most states, it may win under all three rules. In exam questions the rules often differ, which allows the examiner to test your understanding of risk attitude.