# normal form game

A *normal form game* is a game of complete information in which there is a list of $n$ players, numbered $1,\mathrm{\dots},n$. Each player has a strategy set, ${S}_{i}$ and a utility function^{} ${u}_{i}:{\prod}_{i\le n}{S}_{i}\to \mathbb{R}$.

In such a game each player simultaneously selects a move ${s}_{i}\in {S}_{i}$ and receives ${u}_{i}(({s}_{1},\mathrm{\dots},{s}_{n}))$.

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 |