Two-Person Zero-Sum Game/Example/-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:
 * $\map p B = s \paren {s - t} - t \paren {t + s}$