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 that their actions would have on the others players (even if the actor presumed other players would act rationally).
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Although similar, complete and perfect information are not identical. Complete information refers to a state of knowledge about the structure of the game and the objective functions of the players, while not necessarily having knowledge of actions 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 complete, but imperfect, game via the Harsanyi transformation. This simply entails including nature as a player in the game and conditioning payoffs on nature's (unknown) moves.
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.