The maximin criterion is a decision rule in Game Theory where you pick the option with the highest minimum payoff. It fits situations where you do not know what others will do and want the safest worst-case outcome.
The maximin criterion is a decision rule in Game Theory for choices made under uncertainty. You look at each available option, find its worst possible payoff, and then choose the option with the highest of those worst-case outcomes.
That means you are not asking, “What is the biggest payoff I could get?” You are asking, “If things go badly, which option hurts me the least?” In a strategic setting, that mindset makes sense when the other player’s move is unknown, the probabilities are unclear, or you care more about avoiding a bad result than chasing a huge win.
Here is the basic process. First, list the payoff for each strategy against every possible opponent move or state of the world. Next, identify the minimum payoff in each row. Then compare those minimums and pick the row with the largest one. The rule is simple, but the choice reflects a very cautious attitude toward uncertainty.
A quick example makes it easier to see. Suppose Strategy A could give you 10, 4, or -3. Its minimum is -3. Strategy B could give you 6, 5, or 1. Its minimum is 1. A maximin decision maker chooses Strategy B because 1 is better than -3, even though A has a higher best-case payoff.
This is why maximin is often linked to risk aversion. You are protecting yourself from the downside first. In game theory, that can show up when you are unsure whether another player will cooperate, compete, or choose a move that leaves you with very little payoff. The maximin criterion gives you a rule for acting anyway, even without knowing the odds.
The maximin criterion shows how game theory handles uncertainty without relying on exact probabilities. That matters because many real strategic situations are not clean probability problems. You may not know the other player’s beliefs, you may not trust the available information, or the situation may be too messy to assign reliable numbers.
This term also gives you a way to compare different decision rules. Some choices are built around expected value, where you average outcomes using probabilities. Maximin takes a different route and ignores how likely each outcome is. Instead, it asks which option gives the strongest safety net if the worst case happens.
That makes the criterion a useful lens for risk-averse behavior in economics, bargaining, and competitive planning. If a firm is choosing between product strategies, for example, maximin pushes it toward the plan that protects it from the most damaging outcome, even if another plan has a flashier upside.
In a class setting, this term helps you read payoff matrices carefully. You are not just calculating numbers, you are identifying the logic behind the decision rule. Once you can spot maximin, you can also compare it to other criteria like minimax regret or maximax and explain why different decision makers would choose different strategies from the same table.
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view galleryExpected Value
Expected value uses probabilities to find the long-run average payoff of a choice. Maximin does not do that, because it is built for uncertainty when probabilities are unknown or ignored. If a problem gives you likelihoods, expected value may be the better fit. If the problem asks for the safest option, maximin is the move.
Risk Aversion
Risk aversion is the preference for avoiding large losses over chasing large gains. Maximin matches that mindset because it focuses on the worst-case payoff for each option. A risk-averse decision maker often prefers a smaller sure benefit to a strategy that could crash badly, even if the upside looks better.
Maximax Criterion
Maximax is almost the opposite of maximin. Instead of comparing worst-case outcomes, it compares best-case outcomes and chooses the option with the biggest possible payoff. The contrast is useful in game theory because it shows how the same payoff table can lead to very different choices depending on whether you are cautious or optimistic.
Minimax Regret
Minimax regret looks at the disappointment you would feel after making the wrong choice, then tries to reduce the worst possible regret. Maximin is about protecting the worst payoff itself, not the emotional gap between what you chose and what you could have chosen. Both are uncertainty rules, but they measure different kinds of downside.
A problem set question will usually give you a payoff matrix and ask you to choose a strategy under uncertainty. Your job is to find the minimum payoff in each row, compare those minimums, and identify the row with the highest one. If the prompt asks why a decision maker chose that strategy, explain that the maximin criterion favors the safest worst-case outcome.
You may also need to distinguish it from expected value or maximax. A quick written answer should mention that maximin ignores probabilities and reflects a cautious, risk-averse choice. In class discussion or a short essay, you can connect it to uncertainty in bargaining, competition, or planning when outcomes depend on another player’s move.
These two are easy to mix up because both compare payoffs across options. Maximin picks the option with the best worst-case outcome, while maximax picks the option with the best possible outcome. If you are asked for the cautious choice, think maximin. If you are asked for the bold, optimistic choice, think maximax.
Maximin criterion means choosing the option with the highest minimum payoff.
It is a decision rule for uncertainty, not for situations where you know reliable probabilities.
The rule fits a risk-averse mindset because it protects you from the worst-case outcome.
To use it, find each strategy’s minimum payoff first, then compare those minimums.
It is different from expected value and from maximax, which focuses on the best possible payoff.
It is a decision rule where you choose the strategy with the best worst-case payoff. In Game Theory, that means looking at each option’s minimum outcome and then selecting the option with the highest minimum. It is useful when you do not know the other player’s move or cannot trust the probabilities.
Go row by row, find the smallest payoff in each row, and then compare those minimums. The row with the largest minimum value is the maximin choice. This is a common move in uncertainty problems because it shows which strategy protects you best if things go badly.
No. Maximin looks at the worst possible outcome for each option, while maximax looks at the best possible outcome. They often lead to different choices because one is cautious and the other is optimistic. If you remember “min” means downside and “max” means upside, the difference gets easier.
Someone would use it when avoiding a bad outcome matters more than chasing a big reward. That shows up in risky business decisions, bargaining situations, and game theory problems where the opponent’s behavior is uncertain. It is also a good fit when you do not have trustworthy probabilities to plug into expected value.