PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (231)
Orphanage
Unclass'd
Unproven (514)
Corrections (23)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Medium Entry average rating: No information on entry rating
normal form game (Definition)

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$.



"normal form game" is owned by Henry.
(view preamble | get metadata)

View style:

See Also: game

Other names:  strategic form game
Also defines:  normal form game, normal form

Attachments:
examples of normal form games (Example) by Henry
Log in to rate this entry.
(view current ratings)

Cross-references: payoffs, ordered pair, contains, cell, columns, rows, matrix, finite, utility function, strategy, players, complete information, game
There are 2 references to this entry.

This is version 3 of normal form game, born on 2002-07-23, modified 2006-12-17.
Object id is 3191, canonical name is NormalFormGame.
Accessed 7665 times total.

Classification:
AMS MSC: 91A05 (Game theory, economics, social and behavioral sciences :: Game theory :: 2-person games)
 91A06 (Game theory, economics, social and behavioral sciences :: Game theory :: $n$-person games, $n>2$)
 91A10 (Game theory, economics, social and behavioral sciences :: Game theory :: Noncooperative games)
Pending Errata and Addenda
None.
[ View all 2 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)