In economics, perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition. With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market prices, their own utility, and own cost functions. In

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applic ...

, a sequential game 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 (e.g. the starting hands of each player in a card game).Archived a
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Perfect information defined at 0:25, with academic sources and . Perfect information is importantly different from

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, literat ...

of each player's utility functions, payoffs, strategies and "types". A game with perfect information may or may not have complete information. 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, however in some plac ...

and bridge - are examples of games with imperfect information.

Examples

Chess Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to dis ...

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 ( Commonwealth English), or Xs and Os (Canadian or Irish English) is a paper-and-pencil game for two players who take turns marking the spaces in a three-by-three grid with ''X'' or ''O''. ...

, checkers, 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 without ''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 calle ...

(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 nearly 5,000 years to the regions of Mesopotamia and P ...

and

Monopoly A monopoly (from Greek language, Greek el, μόνος, mónos, single, alone, label=none and el, πωλεῖν, pōleîn, to sell, label=none), as described by Irving Fisher, is a market with the "absence of competition", creating a situati ...

. But there are some academic papers which 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 (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...

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

Examples

See also

References

Further reading