Complete information

In economics and game theory, complete information is a term used in to describe an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions, payoffs, strategies and "types" of players are thus common knowledge.

Inversely, in a game with incomplete information, players may not possess full information about their opponents. Some players may possess private information that the others should take into account when forming expectations about how a player would behave.

Complete information is importantly different from perfect information, which implies that each player 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] A game with complete information may or may not have perfect information, and vice-versa.

A game with incomplete information is called a Bayesian game.

Complete vs. perfect information

Complete and perfect information are importantly different. In a game of complete information, the structure of the game and the payoff functions of the players are commonly known but players may not see all of the moves made by other players (for instance, the initial placement of ships inBattleship); there may also be a chance element (as in most card games). Conversely, in games of perfect information, every player observes other players' moves, but may lack some information on others' payoffs, or on the structure of the game.^{[citation needed]}

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

Examples of incomplete but perfect information are conceptually more difficult to imagine. Suppose you are playing a game of chess against an opponent who will be paid some substantial amount of money if a particular event happens (an arrangement of pieces, for instance), but you do not know what the event is. In this case you have perfect information, since you know what each move of the opponent is. However, since you do not know the payoff function of the other player (which will affect its behavior even if it does not alter your own victory conditions), it is a game of incomplete information.

Games of incomplete information arise most frequently in social science rather than as games in the narrow sense.^{[citation needed]} For instance, Harsanyi was motivated by consideration of arms control negotiations, where the players may be uncertain both of the capabilities of their opponents and of their desires and beliefs.

Games of incomplete information can be converted into games of complete but imperfect information under the "common prior assumption." This assumption is commonly made for pragmatic reasons, but its justification remains controversial among economists.

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 6, sect 1)
Gibbons, R. (1992) A primer in game theory. Harvester-Wheatsheaf. (see Chapter 3)

[OsbRub94-Chap6-1] 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-2] Thomas, L. C. (2003). Games, Theory and Applications. Mineola N.Y.: Dover Publications. p. 19. ISBN 0-486-43237-8.

[OsbRub94-Chap11-3] 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.

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v t e Topics in 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
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated 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
Strategies	Backward induction Bid shading Collusion Forward induction Grim trigger Markov strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Bargaining problem Cheap talk Global game Intransitive game Mean-field game Mechanism design n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Stackelberg competition Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers Tic-tac-toe 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 Rock paper scissors Pirate game Dictator game Public goods game Blotto game 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 Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Arrow's impossibility theorem 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
Miscellaneous	All-pay auction Alpha–beta pruning Bertrand paradox Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory First-move advantage in chess Glossary of game theory List of game theorists List of games in game theory No-win situation Solving chess Topological game Tragedy of the commons Tyranny of small decisions

Complete vs. perfect information

See also

References