Definition:Saddle Point (Game Theory)

This page is about saddle point in the context of game theory. For other uses, see Saddle Point.

Definition

Let $G$ be a two-player zero-sum game.

Let $G$ be defined by a payoff table $T$.

Let $E$ be an entry in $T$ such that:

$E$ is the smallest entry in its row

$E$ is the largest entry in its column.

Then $E$ is a saddle point of $G$.

Also see

• Results about saddle points in the context of game theory 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
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): saddle point: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): game theory
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): saddle point: 2.