minimaxcriterium

The minimax criterion, also known as the minimax principle, is a decision-making rule used in decision theory, game theory, statistics, and philosophy. It is employed when the outcomes of decisions are uncertain, and the decision-maker wishes to minimize the possible loss for the worst-case scenario. The principle was first introduced by John von Neumann in 1928.

In game theory, the minimax criterion is used to find the optimal strategy for a player in a zero-sum game, where one player's gain is another player's loss. The minimax strategy involves choosing the action that minimizes the maximum possible loss. This approach assumes that the opponent will always choose the action that maximizes the player's loss.

The minimax criterion can be applied to various fields, including economics, military strategy, and artificial intelligence. In economics, it is used to analyze competitive markets and pricing strategies. In military strategy, it is employed to develop defensive plans that account for potential enemy actions. In artificial intelligence, the minimax algorithm is used to design game-playing programs, such as chess and checkers, that can make optimal decisions.

The minimax criterion is based on the assumption that the decision-maker has complete information about the possible outcomes and the probabilities of those outcomes. However, in many real-world situations, this information may be incomplete or uncertain. In such cases, other decision-making criteria, such as the maximin criterion or the expected utility criterion, may be more appropriate.

In summary, the minimax criterion is a decision-making rule that aims to minimize the possible loss for the worst-case scenario. It is widely used in game theory, economics, military strategy, and artificial intelligence. However, its applicability is limited by the assumption of complete information about the possible outcomes and their probabilities.