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). 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 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.
Card games where each player's cards are hidden from other players but objectives are known, as in contract bridge and poker, would be examples of games with imperfect but complete information if we assume that all players are risk-neutral and thus only maximizing their expected outcome. However, since each individual might respond differently to risk, one cannot generally know the exact form of the objective function the other players are trying to maximize and thus the way they will respond to different situations. Thus, from a purely theoretical perspective, these games should generally be considered as having imperfect and (slighly) incomplete information.
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. 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.
- 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)
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- Ian Frank, David Basin (1997), Artificial Intelligence 100 (1998) 87-123. "Search in games with incomplete information: a case study using Bridge card play".