Perfect information is a concept in

game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

and

economics Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interac ...

that describes a situation where all players in a game or all participants in a market have knowledge of all relevant information in the system. This is different than

complete information In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies ...

, which implies

common knowledge Common knowledge is knowledge that is publicly known by everyone or nearly everyone, usually with reference to the community in which the knowledge is referenced. Common knowledge can be about a broad range of subjects, such as science, litera ...

of each agent's utility functions, payoffs, strategies and "types". A system with perfect information may or may not have complete information. In economics this is sometimes described as "no hidden information" and is a feature of

perfect competition In economics, specifically general equilibrium theory, a perfect market, also known as an atomistic market, is defined by several idealizing conditions, collectively called perfect competition, or atomistic competition. In Economic model, theoret ...

. In a market with perfect information all consumers and producers would have complete and instantaneous knowledge of all market prices, their own utility and cost functions. In game theory, a

sequential game In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that choice before making their own decisions. This turn-based structure, governed by a time axis, d ...

has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the

game A game is a structured type of play usually undertaken for entertainment or fun, and sometimes used as an educational tool. Many games are also considered to be work (such as professional players of spectator sports or video games) or art ...

(e.g. the starting hands of each player in a card game).Archived a
Ghostarchive
and th
Wayback Machine
Perfect information defined at 0:25, with academic sources and . Games where some aspect of play is ''hidden'' from opponents – such as the cards in

poker Poker is a family of Card game#Comparing games, comparing card games in which Card player, players betting (poker), wager over which poker hand, hand is best according to that specific game's rules. It is played worldwide, with varying rules i ...

and

bridge A bridge is a structure built to Span (engineering), span a physical obstacle (such as a body of water, valley, road, or railway) without blocking the path underneath. It is constructed for the purpose of providing passage over the obstacle, whi ...

– are examples of games with imperfect information.

Examples

Chess Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arran ...

is an example of a game with perfect information, as each player can see all the pieces on the board at all times. Other games with perfect information include

tic-tac-toe Tic-tac-toe (American English), noughts and crosses (English in the Commonwealth of Nations, Commonwealth English), or Xs and Os (Canadian English, Canadian or Hiberno-English, Irish English) is a paper-and-pencil game for two players who ta ...

Reversi Reversi is a strategy board game for two players, played on an 8×8 uncheckered board. It was invented in 1883. ''Othello'', a variant with a fixed initial setup of the board, was patented in 1971. Basics Two players compete, using 64 identi ...

checkers Checkers (American English), also known as draughts (; English in the Commonwealth of Nations, Commonwealth English), is a group of Abstract strategy game, strategy board games for two players which involve forward movements of uniform game ...

, and Go. Academic literature has not produced consensus on a standard definition of perfect information which defines whether games with chance, ''but no secret information'', and games with ''simultaneous moves'' are games of perfect information. Games which are

sequential In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called ''elements'', or ''terms''). The number of elements (possibly infinite) is call ...

(players alternate in moving) and which have chance events (with known probabilities to all players) but ''no secret information'', are sometimes considered games of perfect information. This includes games such as

backgammon Backgammon is a two-player board game played with counters and dice on tables boards. It is the most widespread Western member of the large family of tables games, whose ancestors date back at least 1,600 years. The earliest record of backgammo ...

and

Monopoly A monopoly (from Greek language, Greek and ) is a market in which one person or company is the only supplier of a particular good or service. A monopoly is characterized by a lack of economic Competition (economics), competition to produce ...

. However, some academic papers do not regard such games as games of perfect information because the results of chance themselves are unknown prior to them occurring. Games with ''simultaneous moves'' are generally not considered games of perfect information. This is because each player holds information, which is secret, and must play a move without knowing the opponent's secret information. Nevertheless, some such games are

symmetrical Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...

, and fair. An example of a game in this category includes

rock paper scissors Rock, Paper, Scissors (also known by #Names, several other names and word orders) is an Intransitive game, intransitive hand game, usually played between two people, in which each player simultaneously forms one of three shapes with an outstret ...

Examples

See also

References

Further reading