Information about Incomplete Information

Complete information is a term used in economics and game theory to describe an economic situation or game in which knowledge about other market participants or players is available to all participants. Every player knows the payoffs and strategies available to other players.

Complete information is one of the theoretical pre-conditions of an efficient perfectly competitive market. In a sense it is a requirement of the assumption also made in economic theory that market participants act rationally. If a game is not of complete information, then the individual players would not be able to predict the effect their actions would have on the others players (even if the actor presumed other players would act rationally).

Complete vs. perfect information

Although similar, complete and perfect information are not identical. Complete information refers to a state of knowledge about the structure of the game, while not necessarily having knowledge inside the game. So for example, one may have complete information in the context of a Prisoner's Dilemma, but nonetheless this is a game of imperfect information since one does not know the action of the other player. Despite this distinction, it is useful to remember that any game of incomplete information can be transformed, terminology-wise, into a game of imperfect information. One simply includes nature as a player in the game and conditions payoffs on nature's unknown moves.

Examples of incomplete but perfect information are more difficult. 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 it is a game of incomplete information.

Certain information

A distinction is made by some authors of game theory literature between complete and certain information. In this context, complete information is used to describe a game in which all players know the type of all the other players, i.e. they know the payoffs and strategy spaces of the other players. Certain information is used to describe a game in which all players know exactly what game they are playing in the sense that they know what the payoff of playing a particular strategy will be given the strategies played by other players. An equivalent way of making the distinction, particularly helpful in the context of extensive form games, is to define a game of incomplete information as any game in which nature moves first and to define a game of uncertain information as any game in which nature moves after the players have moved.

See also

• market impact

References

• 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)

	Topics in game theory
Definitions	Normal form game Extensive form game Cooperative game Information set Preference
Equilibrium concepts	Nash equilibrium Subgame perfection Bayesian-Nash Perfect Bayesian Trembling hand Proper equilibrium Epsilon-equilibrium Correlated equilibrium Sequential equilibrium Quasi-perfect equilibrium Evolutionarily stable strategy Risk dominance
Strategies	Dominant strategies Mixed strategy Tit for tat Grim trigger Collusion
Classes of games	Symmetric game Perfect information Dynamic game Repeated game Signaling game Cheap talk Zero-sum game Mechanism design Stochastic game Nontransitive game
Games	Prisoner's dilemma Traveler's dilemma Coordination game Chicken Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Minority game Rock, Paper, Scissors Pirate game Dictator game Public goods game Nash bargaining game Blotto games War of attrition
Theorems	Minimax theorem Purification theorems Folk theorem Revelation principle Arrow's theorem