Computational Learning Theory Spring Semester , 2005 / 6 Lecture 7 : May 9

An extensive game is a detailed description of the sequential structure of the decision problems , encountered by the players in strategic situation. There is perfect information in such a game if each player, when making any decision, is perfectly informed of all the events that have previously occurred. • A set of N players • A set H of sequences (finite or infinite): H t : The set of all possible histories up to time t. H = H t Each component of a history is an action taken by a player. • P is the player function, P (h) being the player who takes an action after the history h. After any history h player P (h) chooses an action from the set A(h) = {a : (h, a) ∈ H}. The empty history is the starting point of the game. The game must end eventually. In other words, the length of all items in H is bounded.