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 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 in Battleship); 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.
Games of incomplete information arise most frequently in social science rather than as games in the narrow sense. 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.
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.
- 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)