\begin{definition}[Definition:Profile]
Let $G$ be a game.
Let $N$ be the set of players of $G$.
Let $V$ be a variable defining some aspect of each of the players.
The family of values of $V$ is referred to as a '''profile''', denoted:
:$\family {x_i}_{i \mathop \in N}$
If the fact that $i \in N$ is understood, then $\family {x_i}$ can be used.
\end{definition}