Definition:Payoff Table

Definition
Let $G$ be a two-persongame.

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

$G$ is completely defined by its payoff table.

The two numbers in the entry formed by row $r$ and column $c$ are the payoffs when the row player's moves is $r$ and the column player's moves is $c$.

The first component given is the payoff to the row player.

If the names of the players are $1$ and $2$, the convention is that the row player is player $1$ and the column player is player $2$.

If the names of the players are $\text{A}$ and $\text{B}$, the convention is that the row player is player $\text{A}$ and the column player is player $\text{B}$.

Also known as
A payoff table is also known as a payoff matrix.

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