Definition:Payoff Table/Zero-Sum

Definition

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

A payoff table for $G$ is an array which specifies the payoff to (conventionally) the maximising player for each strategy of both players.

As $G$ is zero-sum, there is no need to specify the payoff to the minimising player, as it will be the negative of the payoff to the maximising player.

		$\text B$
$\text A$		$\begin{array} {r {{|}} c {{|}} } & \text{L} & \text{R} \\ \hline \text{T} & w & x \\ \hline \text{B} & y & z \\ \hline \end{array}$

$G$ is completely defined by its payoff table.

Entry

Each of the values in a payoff table corresponding to the payoff for a combination of a move by each player is called an entry.

Also known as

A payoff table is also known as a payoff matrix.

Some sources hyphenate: pay-off table or pay-off matrix.

Sources

• 1956: Steven Vajda: The Theory of Games and Linear Programming ... (previous) ... (next): Chapter $\text{I}$: An Outline of the Theory of Games: $3$