Perfect information

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, 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.

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]

^ 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.
^ Khomskii, Yurii (2010). "Infinite Games (section 1.1)" (PDF).
^ Archived at Ghostarchive and the Wayback Machine: "Infinite Chess". PBS Infinite Series. March 2, 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155.
^ Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7.
^ 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.

[OsbRub94-Chap6-1] 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.

[Infinite_Games-2] Khomskii, Yurii (2010). "Infinite Games (section 1.1)" (PDF).

[Infinite_chess-3] Archived at Ghostarchive and the Wayback Machine: "Infinite Chess". PBS Infinite Series. March 2, 2017. Perfect information defined at 0:25, with academic sources arXiv:1302.4377 and arXiv:1510.08155.

[mycielski-4] Mycielski, Jan (1992). "Games with Perfect Information". Handbook of Game Theory with Economic Applications. Vol. 1. pp. 41–70. doi:10.1016/S1574-0005(05)80006-2. ISBN 978-0-444-88098-7.

[thomas-5] Thomas, L. C. (2003). Games, Theory and Applications. Mineola New York: Dover Publications. p. 19. ISBN 0-486-43237-8.

[OsbRub94-Chap11-6] 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.

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