# Perfect information

From Wikipedia the free encyclopedia

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 perfect and instantaneous knowledge of all market prices, their own utility, and own 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).^{[1]}^{[2]}^{[3]}^{[4]}

Perfect information is importantly different from complete information, which implies common knowledge of each player's utility functions, payoffs, strategies and "types". A game with perfect information may or may not have complete information.

## Examples[edit]

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 examples of games with perfect information include tic-tac-toe, checkers, infinite chess, and Go.^{[3]}

Card games where each player's cards are *hidden* from other players such as poker and bridge are examples of games with imperfect information.^{[5]}^{[6]}

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.^{[7]}^{[8]}^{[9]}^{[10]}^{[4]}

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. 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.^{[7]}^{[8]}^{[9]}^{[10]}^{[4]}

Games with *simultaneous moves* are generally not considered games of perfect information. This is because each of the players 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.^{[7]}^{[8]}^{[9]}^{[10]}^{[4]}

## See also[edit]

- Complete information
- Extensive form game
- Information asymmetry
- Partial knowledge
- Perfect competition
- Screening game
- Signaling game

## References[edit]

**^**Osborne, M. J.; Rubinstein, A. (1994). "Chapter 6: Extensive Games with Perfect Information".*A Course in Game Theory*. Cambridge, Massachusetts: The MIT Press. ISBN 0-262-65040-1.- ^
^{a}^{b}Khomskii, Yurii (2010). "Infinite Games (section 1.1)" (PDF). - ^
^{a}^{b}"Infinite Chess".*PBS Infinite Series*. March 2, 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155. - ^
^{a}^{b}^{c}^{d}Mycielski, Jan (1992). "Games with Perfect Information".*Handbook of Game Theory with Economic Applications*. Volume 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. **^**Thomas, L. C. (2003).*Games, Theory and Applications*. Mineola New York: Dover Publications. p. 19. ISBN 0-486-43237-8.**^**Osborne, M. J.; Rubinstein, A. (1994). "Chapter 11: Extensive Games with Imperfect Information".*A Course in Game Theory*. Cambridge Massachusetts: The MIT Press. ISBN 0-262-65040-1.- ^
^{a}^{b}^{c}Chen, Su-I Lu, Vekhter. "Game Theory: Rock, Paper, Scissors".CS1 maint: uses authors parameter (link) - ^
^{a}^{b}^{c}Ferguson, Thomas S. "Game Theory" (PDF). UCLA Department of Mathematics. pp. 56–57. - ^
^{a}^{b}^{c}Burch; Johanson; Bowling. "Solving Imperfect Information Games Using Decomposition".*Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence*. - ^
^{a}^{b}^{c}"Complete vs Perfect Information in Combinatorial Game Theory".*Stack Exchange*. June 24, 2014.

## Further reading[edit]

- 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.