Information

A game is of complete information if the payoffs of each player are common knowledge among all the players, and it is of incomplete information if the utility payoffs of each player, or certain parameters to it, remain private information of each player. Games with incomplete information require the players to form beliefs about their opponents' private information, and to evaluate uncertain streams of payoff according to von Neumann-Morgenstern utility function (or some other concept of expected utility).

A game with a perfect information is a game in which at each move in the game, the player with the move knows the full history of the play of the game thus far. Otherwise the game is called a game with imperfect information. In a game of perfect recall, nobody ever forgets something they once knew. An event A is common knowledge if all the players know that A occurred, and all the players know that all the players know that A occurred, and all the players know that all the players know that all the players know that A occurred, and so on, ad infinitum.

Learning process: Consider a repeated play of a finite game. In each period, every player observes the history of past actions, and forms a belief about the other players’ strategies. He then chooses a best response according to his belief about the other players’ strategies. We call such a process a learning process.

Entry by: Aner Sela

November 10, 1997
Direct questions and comments to: Glossary master