Perfect information

A setting in which every player observes all previous actions whenever making a decision. It excludes hidden past moves but does not require players to know opponents’ private information or future choices.

Extensive-form game: A representation of a game using decision points, actions, information sets, and outcomes. Perfect information is defined by how players observe histories in this game representation.
Backward induction: A method for solving finite sequential games by reasoning backward from their final outcomes. With every move observed, players can anticipate optimal responses at later decision points.
Imperfect information: A game setting in which a player cannot distinguish among some possible past histories when choosing an action. It contrasts directly with observing every previous action at each decision.
Combinatorial game theory: The study of mathematical games, often deterministic and sequential, with complete information and no chance moves. Many canonical games studied in this field satisfy perfect-information assumptions.
Game tree: A rooted tree whose nodes represent decision points and whose branches represent actions in a sequential game. A perfect-information game’s tree exposes the path of past actions at each decision point.
Subgame-perfect equilibrium: A strategy profile that forms a Nash equilibrium in every subgame of an extensive-form game. Visible histories identify subgames where planned actions must remain credible.
Incomplete information: A game setting in which at least one player lacks knowledge of another player’s characteristics or preferences. A game can reveal every past move while leaving player types or payoffs unknown.
Go (game): A two-player strategy board game in which players place stones on a grid to control territory. Both players observe the entire board and every move throughout play.
Information set: A collection of decision nodes a player cannot distinguish when choosing an action. Perfect information requires each decision point to be distinguishable from every other possible history.
Nash equilibrium: A strategy profile in which no player can gain by changing strategy alone. It provides the equilibrium benchmark, though it may admit noncredible plans in sequential games.

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