\begin{definition}[Definition:Game/Payoff]
The '''payoff''' of a '''game''' is the reward or punishment made to a '''player''' at the end of the '''game''' as a result of combination of the various strategies employed.
Let $G$ be a game.
Let $N$ be the set of players of $G$.
Let $A$ be the set of moves available to player $i \in N$.
Let $u_i: A \to \R$ be a the payoff function on $A$.
A '''payoff''' is the value of $u_i$ for a given $a \in A$.
\end{definition}