A normal form game is a game of complete information in which there is a list of $n$ players, numbered $1,\ldots,n$ Each player has a strategy set, $S_i$ and a utility function $u_i:\prod_{i\leq n} S_i\rightarrow \mathbb{R}$

In such a game each player simultaneously selects a move $s_i\in S_i$ and receives $u_i((s_1,\ldots,s_n))$

Normal form games with two players and finite strategy sets can be represented in normal form, a matrix where the rows each stand for an element of $S_1$ and the columns for an element of $S_2$ Each cell of the matrix contains an ordered pair which states the payoffs for each player. That is, the cell $i,j$ contains $(u_1(s_i,s_j),u_2(s_i,s_j))$ where $s_i$ is the $i$ th element of $S_1$ and $s_j$ is the $j$ th element of $S_2$