Complete information and incomplete information are terms widely used in economics, especially game theory and behavioural economics. We say that there is complete information when each agent knows the other agent’s utility function and the rules of the game. As Luce and Raiffa put it in their “Games and Decisions: Introduction and Critical Survey“, 1957, complete information, understood as the situation where “each player is fully aware of the rules of the game and the utility functions of each of the players”, is a central assumption of game theory. However, this situation and its definition does not consider the awareness of each player, which is covered by the term “common knowledge“, which means that each player is aware that the other players know the rules and every utility function.
Incomplete information, also known as asymmetric information, refers to the contrary, where not all players know each other’s utility functions. John Harsanyi developed the theory of incomplete information in his “Games with Incomplete Information Played by ‘Bayesian’ Players”, 1967.