Perfect information

In economics, perfect information is a feature of perfect competition. With perfect information in a market, all consumers and producers are assumed to have perfect knowledge of price, utility, quality and production methods of products, when theorizing the systems of free markets, and effects of financial policies.

In game theory, an extensive-form 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]

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, and vice versa; however, when a game is described as having perfect information, complete information is often assumed, unless specified otherwise.

Examples

Backgammon is an example of a game with perfect information that involves chance. Both players are completely aware of the state of the game at all times and can use this to inform their decisions, but the progress of the game will depend on random dice rolls.

Texas hold'em is a game of imperfect information, as players do not know the private cards of their opponents

Chess is an example of a game with perfect information as each player can ostensibly see all of the pieces on the board at all times. Other examples of perfect games include tic-tac-toe, Irensei, and Go. The formal definition can be easily extended to include games with exogenous uncertainty from chance events, such as in backgammon, or simultaneous move games, such as in the iterated prisoner's dilemma, or both, such as in Goofspiel.

Card games where each player's cards are hidden from other players, as in contract bridge and poker, are examples of games with imperfect information.^[2]^[3]

References

↑ Osborne, M. J.; Rubinstein, A. (1994). "Chapter 6: Extensive Games with Perfect Information". A Course in Game Theory. Cambridge M.A.: The MIT Press. ISBN 0-262-65040-1.
↑ Thomas, L. C. (2003). Games, Theory and Applications. Mineola N.Y.: 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 M.A.: The MIT Press. ISBN 0-262-65040-1.

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.

Topics in game theory

Definitions	Normal-form game Extensive-form game Escalation of commitment Graphical game Cooperative game Succinct game Information set Hierarchy of beliefs Preference

Equilibrium concepts	Nash equilibrium Subgame perfection Mertens-stable equilibrium Bayesian Nash equilibrium Perfect Bayesian equilibrium Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance Core Shapley value Pareto efficiency Gibbs equilibrium Quantal response equilibrium Self-confirming equilibrium Strong Nash equilibrium Markov perfect equilibrium

Strategies	Dominant strategies Pure strategy Mixed strategy Tit for tat Grim trigger Collusion Backward induction Forward induction Markov strategy

Classes of games	Symmetric game Perfect information Simultaneous game Sequential game Repeated game Signaling game Screening game Cheap talk Zero-sum game Mechanism design Bargaining problem Stochastic game n-player game Large Poisson game Nontransitive game Global games Strictly determined game Potential game

Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock-paper-scissors Pirate game Dictator game Public goods game Blotto games War of attrition El Farol Bar problem Fair division Fair cake-cutting Cournot game Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Prisoners and hats puzzle Trust game Princess and monster game Monty Hall problem Rendezvous problem

Theorems	Minimax theorem Nash's theorem Purification theorem Folk theorem Revelation principle Arrow's impossibility theorem

Key figures	Albert W. Tucker Amos Tversky Ariel Rubinstein Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin Jean Tirole Jean-François Mertens John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Thomas Schelling William Vickrey

See also	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons Tyranny of small decisions

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Perfect information

Examples

See also

References

Further reading