Editing Perfect information

{{Short description|Condition in economics and game theory}}
[[File:Final_Position_of_Lawrence-Tan_2002.png|thumb|[[Chess]] is an example of a game of perfect information.]]
'''Perfect information''' is a concept in [[game theory]] and [[economics]] 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]], which implies [[Common knowledge (logic)|common knowledge]] 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 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]] 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).<ref name="OsbRub94-Chap6">{{cite book|title=A Course in Game Theory|last2=Rubinstein|first2=A.|publisher=The MIT Press|year=1994|isbn=0-262-65040-1|location=Cambridge, Massachusetts|chapter=Chapter 6: Extensive Games with Perfect Information|last1=Osborne|first1=M. J.}}</ref><ref name="Infinite Games">{{cite web |url=https://www.math.uni-hamburg.de/home/khomskii/infinitegames2010/Infinite%20Games%20Sofia.pdf |first=Yurii |last=Khomskii |date=2010 |title=Infinite Games (section 1.1) }}</ref><ref name="Infinite chess">Archived at [https://ghostarchive.org/varchive/youtube/20211211/PN-I6u-AxMg Ghostarchive]{{cbignore}} and the [https://web.archive.org/web/20170302182305/https://www.youtube.com/watch?v=PN-I6u-AxMg&gl=US&hl=en Wayback Machine]{{cbignore}}: {{cite web |url=https://www.youtube.com/watch?v=PN-I6u-AxMg&t=0m25s |title=Infinite Chess |work=PBS Infinite Series |date=March 2, 2017 }}{{cbignore}} Perfect information defined at 0:25, with academic sources {{ArXiv|1302.4377}} and {{ArXiv|1510.08155}}.</ref><ref name="mycielski">{{cite book |last=Mycielski |first=Jan |title=Handbook of Game Theory with Economic Applications |year=1992 |isbn=978-0-444-88098-7 |volume=1 |pages=41–70 |chapter=Games with Perfect Information |doi=10.1016/S1574-0005(05)80006-2 |author-link=Jan Mycielski}}</ref>

[[File:Texas Hold 'em Hole Cards.jpg|thumb|right|[[Poker]] is a game of imperfect information, as players do not know the private cards of their opponents.]]
Games where some aspect of play is ''hidden'' from opponents – such as the cards in [[poker]] and [[contract bridge|bridge]] – are examples of games with '''imperfect information'''.<ref name="thomas">{{cite book
  | last = Thomas
  | first = L. C.
  | title = Games, Theory and Applications
  | url = https://archive.org/details/gamestheoryappli0000thom
  | url-access = limited
  | publisher = Dover Publications
  | year = 2003
  | location = Mineola New York
  | page = [https://archive.org/details/gamestheoryappli0000thom/page/n18 19]
  | isbn = 0-486-43237-8}}
</ref><ref name="OsbRub94-Chap11">{{cite book
  | last1 = Osborne
  | first1 = M. J.
  | last2 = Rubinstein
  | first2 = A.
  | title = A Course in Game Theory
  | chapter = Chapter 11: Extensive Games with Imperfect Information
  | publisher = The MIT Press
  | year = 1994
  | location = Cambridge Massachusetts
  | isbn = 0-262-65040-1}}
</ref>

==Examples==
[[File:Backgammon lg.png|thumb|right|[[Backgammon]] includes chance events, but by some definitions is classified as a game of perfect information.]]
[[Chess]] is an example of a game with perfect information, as each player can see all the pieces on the board at all times.<ref name="Infinite Games"/> Other games with perfect information include [[tic-tac-toe]], [[Reversi]], [[Draughts|checkers]], and [[Go (game)|Go]].<ref name="Infinite chess"/>

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 game|''simultaneous moves'']] are games of perfect information.<ref name="mycielski" /><ref name="stanford">{{cite web |url=https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/psr.html |title=Game Theory: Rock, Paper, Scissors  |author=Janet Chen |author2=Su-I Lu |author3=Dan Vekhter |website=cs.stanford.edu}}</ref><ref name="ucla">{{cite web |url=https://www.math.ucla.edu/~tom/Game_Theory/mat.pdf#page=56 |title=Game Theory |first=Thomas S. |last=Ferguson|author-link= Thomas S. Ferguson |pages=56–57 |publisher=UCLA Department of Mathematics }}</ref><ref name="aaai">{{cite web |url=https://www.aaai.org/ocs/index.php/AAAI/AAAI14/paper/viewFile/8407/8476 |title=Solving Imperfect Information Games Using Decomposition |last1=Burch |last2=Johanson |last3=Bowling |work=Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence }}</ref>

Games which are [[Sequential game|sequential]] (players alternate in moving) and which have [[move by nature|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]] and [[Monopoly (game)|Monopoly]]. 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.<ref name="mycielski" /><ref name="stanford"/><ref name="ucla"/><ref name="aaai"/>

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 [[Symmetric game|symmetrical]], and fair. An example of a game in this category includes [[rock paper scissors]].<ref name="mycielski" /><ref name="stanford"/><ref name="ucla"/><ref name="aaai"/>

==See also==
*[[Extensive form game]]
*[[Information asymmetry]]
*[[Dispersed knowledge|Partial knowledge]]
*[[Screening game]]
*[[Signaling game]]

==References==
{{reflist}}

==Further reading==
* Fudenberg, D. and [[Jean Tirole|Tirole, J.]] (1993) ''Game Theory'', [[MIT Press]]. (see Chapter 3, sect 2.2)
* Gibbons, R. (1992) ''A primer in game theory'', Harvester-Wheatsheaf. (see Chapter 2)
* [[R. Duncan Luce|Luce, R.D.]] and [[Howard Raiffa|Raiffa, H.]] (1957) ''Games and Decisions: Introduction and Critical Survey'', Wiley & Sons (see Chapter 3, section 2)
* [https://mises.org/library/economics-groundhog-day The Economics of ''Groundhog Day''] by economist D.W. MacKenzie, using the 1993 film ''[[Groundhog Day (film)|Groundhog Day]]'' to argue that perfect information, and therefore perfect competition, is impossible.
* Watson, J. (2013) ''Strategy: An Introduction to Game Theory'', W.W. Norton and Co.
{{game theory}}

{{DEFAULTSORT:Perfect Information}}
[[Category:Game theory]]
[[Category:Perfect competition]]
[[Category:Board game terminology]]