1 Extensive Games with Perfect Information
7.1.1 Definitions Definition An extensive game with perfect information 〈N, H, P, Ui〉 has the following components: • A set of N players • A set H of sequences (finite or infinite). each member of H is a history; each component of a history ia an action taken by a player. • P is the player function, P (h) being the player who takes an action after the history h. • Payoff function Ui, i ∈ N 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.