## 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.