Two-Person Zero-Sum Game/Examples/-1, 0, 1

Example of Two-Person Zero-Sum Game

The two players are $A$ and $B$.

$A$ and $B$ each have three possible moves, the values:

$-1, 0, 1$

Let $A$'s move be $s$.

Let $B$'s move be $t$.

Then the payoff to $A$ is given by:

$\map p A = s \paren {t - s} + t \paren {t + s}$

As $G$ is zero-sum it follows that the payoff to $A$ is given by:

$\map p B = s \paren {s - t} - t \paren {t + s}$

Payoff Table

		$\text B$
$\text A$		$\begin {array} {r {{|}} c {{|}}} & -1 & 0 & 1 \\ \hline -1 & 2 & -1 & -2 \\ \hline 0 & 1 & 0 & 1 \\ \hline 1 & -2 & -1 & 2 \\ \hline \end{array}$

Sources

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