= Solution
A <game tree> is a rooted <tree> representing successive histories. A nonterminal <vertex> specifies the player who moves, its outgoing <edges> are the available actions, and each leaf specifies a terminal <payoff> for every player. A <pure strategy> specifies an action at every decision point belonging to that player, including decision points not reached by the eventual play.
For a <perfect-information game>, each player observes the exact preceding history. An <extensive-form game> with imperfect information additionally groups indistinguishable decision points into <information sets>, with compatible available actions. Chance moves, if present, carry specified <probabilities>; the displayed game has none. A <subgame perfect equilibrium> must prescribe a <Nash equilibrium> in every proper subgame as well as in the whole <game>.
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