maxmin

Maxmin, often written as max-min or maximin, is a shorthand used in mathematics and decision theory for selecting decisions or strategies by focusing on the best outcome achievable under the worst-case scenario. The core idea is robustness: to optimize the smallest guaranteed payoff.

In decision theory, the maximin criterion asks a decision-maker to choose the option whose worst-case payoff is as large as possible. It describes a pessimistic or conservative attitude, in contrast to the optimistic maximax criterion or to expected-value approaches.

In game theory, a maximin strategy for a player guarantees the highest possible minimum payoff given the other players’ strategies. In two-player zero-sum games, the maximin value equals the minimax value by the minimax theorem, which ensures the existence of a saddle point in mixed strategies.

In optimization and computer science, max-min problems can refer to maximizing the minimum value of a set of objectives or variables. They arise in robust optimization, fair resource allocation, and max-min fairness in networks, where the goal is to improve the least-served user or component. Solvers convert these problems into linear or convex programs using auxiliary variables and reformulations.

Notes: The term is used in various spellings, including max-min, maximin, and maxmin. Clarifying the context is important to determine the exact meaning in a given field.