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]

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]^[10]

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

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]^[10]

References

^ 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 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.
^ ^a ^b ^c ^d 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.
^ ^a ^b ^c Janet Chen; Su-I Lu; Dan Vekhter. "Game Theory: Rock, Paper, Scissors".
^ ^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.

v t e Topics of game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game Mechanism design
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Coalition-proof Nash equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand equilibrium
Strategies	Appeasement Backward induction Bid shading Collusion Cheap talk De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Pairing strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Auction Bargaining problem Global game Intransitive game Mean-field game n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers All-pay auction Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Electronic mail game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Bertrand competition Cournot competition Stackelberg competition Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Search optimizations	Alpha–beta pruning Aspiration window Principal variation search max^n algorithm Paranoid algorithm Lazy SMP
Miscellaneous	Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory Glossary of game theory List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons

Perfect information

Examples

See also

References

Further reading