Payoff Table/Examples

Examples of Payoff Tables

Arbitrary Example

Consider a two-person game $G$ with players are $\text A$ and $\text B$ such that:

player $\text A$ make make any of $3$ moves

player $\text B$ make make any of $4$ moves.

The payoff table for player $\text A$ will be in the form:

		$\text B$
$\text A$		$\begin {array} {r {{|}} c {{|}} } & 1 & 2 & 3 & 4 \\ \hline 1 & a_{1 1} & a_{1 2} & a_{1 3} & a_{1 4} \\ \hline 2 & a_{2 1} & a_{2 2} & a_{2 3} & a_{2 4} \\ \hline 3 & a_{3 1} & a_{3 2} & a_{3 3} & a_{3 4} \\ \hline \end {array}$

Here, $a_{i j}$ is the amount $\text A$ wins if $\text A$ makes move $i$ and $\text B$ makes move $j$.

If $G$ is a zero-sum game, then player $\text B$'s payoff table will be the same as for player $\text A$, but with $a_{i j}$ replaced with $-a_{i j}$.