Perfect information: Difference between revisions
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| caption2 = [[Poker]] is a game of imperfect information as opponents' private cards are not known | |||
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'''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. | '''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 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 " | 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 "initialisation 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> | ||
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 | 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 | | last = Thomas | ||
Latest revision as of 09:03, 19 June 2025
Template:Short descriptionTemplate:Multiple image
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 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 "initialisation event" of the game (e.g. the starting hands of each player in a card game).[1][2][3][4]
Games where some aspect of play is hidden from opponents – such as the cards in poker and bridge – are examples of games with imperfect information.[5][6]
Examples
Chess is an example of a game with perfect information, as each player can see all the pieces on the board at all times.[2] Other games with perfect information include tic-tac-toe, Reversi, checkers, and Go.[3]
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.[4][7][8][9]
Games which are sequential (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 and 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.[4][7][8][9]
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, and fair. An example of a game in this category includes rock paper scissors.[4][7][8][9]
See also
References
Further reading
- Fudenberg, D. and 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)
- Luce, R.D. and Raiffa, H. (1957) Games and Decisions: Introduction and Critical Survey, Wiley & Sons (see Chapter 3, section 2)
- The Economics of Groundhog Day by economist D.W. MacKenzie, using the 1993 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.
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- ↑ a b Script error: No such module "citation/CS1".
- ↑ a b Archived at GhostarchiveTemplate:Cbignore and the Wayback MachineTemplate:Cbignore: Script error: No such module "citation/CS1".Template:Cbignore Perfect information defined at 0:25, with academic sources arXiv:1302.4377File:Lock-green.svg and arXiv:1510.08155File:Lock-green.svg .
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