Definition:Maximin Strategy

Definition

Let $G$ be a two-person game between players $A$ and $B$.

A maximin strategy for $A$ is one in which:

$(1): \quad A$ assumes that $B$ will make that move which makes $A$'s payoff (or average payoff, in the case of a random element) as small as possible.

$(2): \quad A$ then makes the move which makes this smallest gain the largest possible.

Hence it is the strategy that will maximise $A$'s minimum payoff.

The reasoning is:

I fear that my opponent will make the move which makes my payoff the smallest possible. Hence I make my move so as to make this smallest payoff as large as possible.

Also known as

A maximin strategy is also known as a maximin criterion.

Also see

• Results about maximin strategies can be found here.

Sources

• 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $3$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): game theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory