Extensive-form game

A game-theoretic model that represents players’ possible actions, move order, information at each decision, and outcomes in a game tree.

Game tree: A branching diagram of decision points, actions, and outcomes in a sequential process. It displays the histories and terminal outcomes that define the game's structure.
Subgame: A portion of a game tree that begins at a decision node and contains all its successors without splitting information sets. Subgames isolate continuations that can be analyzed as games in their own right.
Strategic-form game: A representation listing players, complete strategies, and payoffs for every strategy profile. It compresses the move sequence into whole-game strategy choices.
Ultimatum game: A bargaining game in which one player proposes a division and another accepts or rejects it. Its proposal and response form a simple sequential game tree.
Decision node: A point in a game tree where a player chooses an action. Each such node identifies who moves and which actions are available.
Subgame-perfect equilibrium: A strategy profile that forms a Nash equilibrium in every subgame. It rules out plans relying on noncredible threats in later branches.
Normal-form representation: A payoff table encoding a game through players' strategies and resulting outcomes. It can represent the same incentives while hiding timing and information.
Centipede game: A sequential game in which players alternate between ending play and passing to the next move. Its long chain of decisions exposes tensions between backward induction and observed behavior.
Information set: A set of decision nodes that a player cannot distinguish when choosing an action. It encodes what the moving player knows at that point.
Backward induction: A method for solving finite games by reasoning from final decisions toward earlier ones. It derives choices by resolving the tree from its terminal outcomes backward.

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