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 $u_i:{\prod }_{i\le n}{S}_i\to ℝ$.

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