Definition:Game/Payoff

Definition
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 $a \in A$.

Also known as
Some sources hyphenate: pay-off.