minmaks

Minmaks is a term used in optimization, decision theory, and game theory to describe a strategy or solution that guards against the worst-case outcome by minimizing the maximum possible loss or cost. In English and many technical texts the standard form is minimax, but in some languages the spelling minmaks is used. The core idea is to prepare for the most adverse scenario.

In two-player zero-sum games, the minimax principle leads to strategies that minimize the opponent's best possible payoff. The minimax algorithm is a recursive method for evaluating game trees: at each node, the algorithm selects the move that minimizes the maximum payoff for the opponent (or equivalently maximizes the player's own minimum guarantee). Alpha-beta pruning improves efficiency by skipping branches that cannot influence the final decision.

In optimization, min-max or robust optimization seeks decisions that perform well under worst-case input or disturbances, often formulated as min_x max_y f(x,y). Duality relates minmax to maxmin under certain conditions and can reveal saddle points.

Variants include maximin (maximize the minimum payoff) and saddle-point concepts. Applications span artificial intelligence (game playing and planning), control systems, economics and finance (robust decision-making), and operations research.

History: the foundations trace to early 20th-century game theory, notably von Neumann’s minimax theorem, establishing the existence of equilibrium in zero-sum games. The term “minimax/minmaks” remains standard across diverse fields, with context determining whether the emphasis is on the minimization of loss or the maximization of guaranteed payoff.