Extensive-Form Game
A representation of sequential play using a rooted tree with information sets.
Definition
A tuple : tree with precedence , player function , information partition and payoffs on terminal nodes.
A pure strategy specifies an action at every information set; behavior strategies assign distributions over actions per info set.
Intuition
Models who moves when and what each player knows at the time of their move.
Strategic and extensive forms are equivalent for strategic-form analysis but extensive form captures timing and information.
Worked example
The Centipede Game, Stackelberg leader-follower, and sequential bargaining are extensive form.
Any chess position is a node in the extensive-form game of chess.
The math
Kuhn's theorem: in games of perfect recall, mixed and behavior strategies are outcome-equivalent.
Zermelo (1913) showed finite perfect-information games have a pure-strategy backward-induction solution.
Where it is used
Used to analyze negotiations, repeated interactions, and multi-stage mechanism design.
Backward induction and subgame perfection are natural here.
More in Game theory
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