Maximax criterion

The maximax criterion is a decision rule in Game Theory where you choose the option with the highest possible payoff. It assumes an optimistic, risk-seeking stance and ignores the worst-case outcomes.

What is the maximax criterion?

The maximax criterion is a way to make decisions under uncertainty in Game Theory by choosing the option with the best possible payoff. You look at each action, find its highest possible outcome, and then pick the action with the single biggest upside.

This makes maximax the most optimistic decision rule in the topic of decision-making under uncertainty. It does not ask which outcome is most likely, and it does not protect you from bad results. It just says, "If everything goes really well, which choice gives me the most?"

A payoff matrix is the easiest way to see it. Suppose one strategy can pay 8, another can pay 20, and another can pay 15 in their best cases. The maximax criterion chooses the strategy with 20, even if that same strategy has a terrible downside in other states of the world.

That is why maximax is different from expected value. Expected value uses probabilities, while maximax ignores probabilities entirely. It is also different from maximin, which looks at the worst case instead of the best case. In a game theory class, this difference shows how people can make very different choices when the same uncertain payoff table is on the page.

Maximax is most useful when the decision-maker is strongly risk-seeking or when the upside matters more than avoiding losses. It can also show up in classroom examples where a player, firm, or investor is acting on pure hope rather than on a careful estimate of likely outcomes. In real strategic settings, that can be bold, but it can also be reckless.

Why the maximax criterion matters in Game Theory

Maximax matters because it gives you one clear way to read choices in uncertain games, especially when probabilities are missing or unreliable. In Game Theory, that matters a lot because many real decisions happen before you know what the other player will do, what the market will do, or which state of nature will appear.

This criterion also helps you see the difference between a decision rule and a prediction. Maximax is not saying the best outcome will happen, only that the decision-maker is acting as if the best case is the one worth chasing. That makes it useful for analyzing risk-loving behavior, aggressive business moves, or strategic choices that aim for a big payoff.

It also sets up comparison questions. Once you know maximax, you can explain why someone else might prefer maximin, minimax regret, or expected value instead. That comparison is a big part of this topic, because decision-making under uncertainty is really about how people deal with missing information, risk, and regret.

How the maximax criterion connects across the course

maximin criterion

Maximin is the main contrast to maximax. Instead of looking for the best possible payoff, maximin looks at each option’s worst possible payoff and chooses the safest one. If maximax is the optimistic rule, maximin is the cautious rule, so comparing them tells you a lot about the decision-maker’s attitude toward risk.

expected value

Expected value adds probabilities into the decision. That means a choice with a huge best-case payoff is not automatically preferred if the payoff is unlikely. Maximax ignores those probabilities completely, so it can point to a very different answer than expected value on the same payoff table.

minimax regret

Minimax regret asks which choice would leave you with the smallest possible feeling of having chosen badly after the outcome is known. That is a different question from maximax, which only cares about the highest payoff. The two rules can lead to different answers because regret focuses on comparison with the outcome you missed.

decision tree

A decision tree can organize the same uncertainty that a payoff matrix shows. You can trace branches, outcomes, and payoffs, then apply a rule like maximax by checking which branch has the biggest upside. It is a useful visual when the problem is more complicated than a simple table.

Is the maximax criterion on the Game Theory exam?

A problem set or quiz item will usually give you a payoff matrix and ask which option the maximax criterion selects. Your job is to scan each strategy, identify its best possible payoff, and then pick the strategy with the largest of those maxima. You are not calculating probabilities, and you are not checking the worst-case outcome.

If the question is a compare-and-contrast item, explain that maximax is the optimistic rule, while maximin is the conservative one. If the prompt uses a word problem, translate the story into payoffs first, then apply the rule to the table or decision tree. The main mistake to avoid is mixing maximax with expected value, since maximax does not average outcomes at all.

The maximax criterion vs maximin criterion

These two are commonly mixed up because both are decision rules under uncertainty. Maximax chooses the option with the highest best-case payoff, while maximin chooses the option with the highest worst-case payoff. If you remember "best case" for maximax and "worst case" for maximin, the difference becomes much easier to spot on a payoff table.

Key things to remember about the maximax criterion

• Maximax is the most optimistic decision rule in Game Theory because it chooses the option with the highest possible payoff.

• You apply it by checking each strategy’s best outcome, then selecting the strategy with the largest maximum payoff.

• The rule ignores probabilities and ignores downside risk, so it can produce bold but fragile choices.

• Maximax is the opposite style of maximin, which protects against the worst case instead of chasing the biggest upside.

• When you see a payoff matrix or decision tree, maximax asks, “Which choice could pay off the most if everything goes right?”

Frequently asked questions about the maximax criterion

What is maximax criterion in Game Theory?

The maximax criterion is a decision rule that chooses the option with the highest possible payoff. It is used in Game Theory when outcomes are uncertain and the decision-maker is acting very optimistically. The rule ignores probabilities and focuses only on the best-case result for each option.

How do you use maximax on a payoff matrix?

First, look at the highest payoff in each row or for each strategy. Then compare those best-case values and choose the largest one. That is the maximax choice. You do not average the outcomes, and you do not worry about the worst payoff.

What is the difference between maximax and maximin?

Maximax looks at the best possible payoff for each option and picks the biggest one. Maximin looks at the worst possible payoff for each option and picks the safest one. So maximax is optimistic and risk-seeking, while maximin is cautious and protective.

When would someone use maximax?

Someone might use maximax when they care most about a huge upside and are willing to accept serious risk. In Game Theory, that can describe a player, business, or decision-maker who is chasing the best possible outcome even if the downside is large. It is useful as a model of behavior, but it is not always the safest choice.