# normal form game

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 $S_{2}$.

 Title normal form game Canonical name NormalFormGame Date of creation 2013-03-22 12:51:24 Last modified on 2013-03-22 12:51:24 Owner Henry (455) Last modified by Henry (455) Numerical id 6 Author Henry (455) Entry type Definition Classification msc 91A10 Classification msc 91A06 Classification msc 91A05 Synonym strategic form game Related topic Game Defines normal form game Defines normal form