Editing Game theory (section)

===Perfect information and imperfect information===
{{main|Perfect information}}
[[File:PD with outside option.svg|thumb|upright=1.25|right|A game of imperfect information. The dotted line represents ignorance on the part of player 2, formally called an [[Information set (game theory)|information set]].]]

An important subset of sequential games consists of games of perfect information. A game with perfect information means that all players, at every move in the game, know the previous history of the game and the moves previously made by all other players. An imperfect information game is played when the players do not know all moves already made by the opponent such as a simultaneous move game.<ref name=":2" /> Examples of perfect-information games include [[tic-tac-toe]], [[Draughts|checkers]], [[chess]], and [[Go (board game)|Go]].<ref>{{cite web |url=https://www.math.ucla.edu/~tom/Game_Theory/mat.pdf#page=56 |archive-url=https://web.archive.org/web/20040730140255/http://www.math.ucla.edu/~tom/Game_Theory/mat.pdf |archive-date=2004-07-30 |url-status=live |title=Game Theory |first=Thomas S. |last=Ferguson|author-link= Thomas S. Ferguson |pages=56–57 |publisher=UCLA Department of Mathematics}}</ref><ref>{{cite book |first=Jan |last=Mycielski |author-link=Jan Mycielski |chapter=Games with Perfect Information |title=Handbook of Game Theory with Economic Applications |volume=1 |year=1992 |pages=41–70 |doi=10.1016/S1574-0005(05)80006-2 |isbn=978-0-4448-8098-7}}</ref><ref>{{cite web |url=https://www.youtube.com/watch?v=PN-I6u-AxMg&t=0m25s | archive-url=https://ghostarchive.org/varchive/youtube/20211028/PN-I6u-AxMg| archive-date=2021-10-28|title=Infinite Chess |work=PBS Infinite Series |date=2 March 2017 }}{{cbignore}} Perfect information defined at 0:25, with academic sources {{ArXiv|1302.4377}} and {{ArXiv|1510.08155}}.</ref>

Many card games are games of imperfect information, such as [[poker]] and [[contract bridge|bridge]].<ref>{{Cite book |title=Game Theory: Third Edition |last=Owen |first=Guillermo |publisher=Emerald Group Publishing |year=1995 |isbn=978-0-12-531151-9 |location=Bingley |page=4}}</ref> Perfect information is often confused with [[complete information]], which is a similar concept pertaining to the common knowledge of each player's sequence, strategies, and payoffs throughout gameplay.<ref>{{cite book |doi=10.1007/978-1-349-20181-5_22 |chapter=Perfect Information |title=Game Theory |date=1989 |last1=Mirman |first1=Leonard J. |pages=194–198 |isbn=978-0-333-49537-7 }}</ref> Complete information requires that every player know the strategies and payoffs available to the other players but not necessarily the actions taken, whereas perfect information is knowledge of all aspects of the game and players.<ref>{{Cite book|last=Mirman|first=Leonard|title=Perfect Information|publisher=Palgrave Macmillan|year=1989|isbn=978-1-349-20181-5|location=London|pages=194–195}}</ref> Games of [[Information asymmetry|incomplete information]] can be reduced, however, to games of imperfect information by introducing "[[Move by nature|moves by nature]]".{{sfnp|Shoham|Leyton-Brown|2008|p=60}}