What is "normal form game"

n. (context game theory English) Formally, a structure $(P,\; mathbf\{S\},\; mathbf\{F\})$ where ''P'' = {1,2, ...,''m''} is a set of players, $mathbf\{S\}=\; (S\_1,\; S\_2,\; ldots,\; S\_m)$ is an ''m''-tuple of pure strategy sets, one for each player, and $mathbf\{F\}\; =\; (F\_1,\; F\_2,\; ldots,\; F\_m)$ is an ''m''-tuple of payoff functions.