Perfect Information¶
In an extensive-form game, every decision maker can identify the exact history at each turn, so every decision information set is a singleton.
Core Idea¶
A sequential extensive-form game has perfect information if every player at each turn can distinguish the exact decision node reached: every information set is a singleton. It concerns observed history, not knowledge of future choices or all payoff parameters. In a finite perfect-information game with specified payoffs, backward induction yields at least one pure-strategy subgame-perfect equilibrium; this is a conditional theorem, not the definition.[^ref-2e50c88890b1]
Scope of Application¶
In Ozdaglar's stylized entry-deterrence game, the incumbent observes entry before choosing Accommodate or Fight; backward induction with the lecture's payoffs gives In and Accommodate. In its two-stage matching-pennies comparison, the second player can condition a move on an observed H or T; joining those two nodes into one hidden-action information set changes the model to imperfect information while keeping terminal payoff labels. These are game-tree examples, not reported market behavior.[^ref-2e50c88890b1]
Clarity¶
Check the mover's information set at every decision. Known payoffs (complete information) do not imply observed earlier choices (perfect information). Market “perfect information” about price or product quality is an adjacent, looser usage, not an automatic singleton-set condition. The finite equilibrium theorem does not mean large games are practically solved or that infinite games satisfy the same claim without further assumptions.[ref-2e50c88890b1][ref-3b262610163a]
Manages Complexity¶
Singleton sets allow separate contingent choices after each visible history. Backward induction works from terminal nodes toward the root, including off-path subgames, but a game tree can still be computationally enormous. Concealing a prior move removes the later player's ability to condition on that branch, as the matching-pennies contrast shows.[^ref-2e50c88890b1]
Abstract Reasoning¶
Draw the tree, mark who moves, then partition each mover's decision nodes by what that mover can distinguish. All singleton sets give perfect information; any non-singleton set is a counterexample. For finite specified-payoff games, optimize terminal continuations backward, allowing ties and retaining off-path choices. Observability may help one actor tailor a response while disclosure may expose another to that tailoring.[^ref-2e50c88890b1]
Knowledge Transfer¶
The live Information prime supplies a broad idea of available distinctions. Here the condition concerns information sets over histories in a formal extensive game. Live Game requires played activity, while Game Form is an action-profile-to-outcome structure without payoffs and does not itself supply this history partition. The condition should not be imported into market transparency or conflated with subgame perfection.[ref-2e50c88890b1][ref-3b262610163a]
[^ref-2e50c88890b1]: Asu Ozdaglar, MIT 6.254 Lecture 12, pp. 4, 9–13, 19–22. [^ref-3b262610163a]: MIT 17.810 Lecture 4, pp. 25–27 and 37–38.
Neighborhood in Abstraction Space¶
Perfect Information sits in a moderately populated region (56th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Game-Theoretic Models & Paradoxes (37 abstractions)
Nearest neighbors
- Cognitive Hierarchy Theory — 0.86
- Bayesian Nash Equilibrium — 0.85
- Subgame Perfect Equilibrium — 0.85
- Game complexity — 0.85
- Centipede Game — 0.85
Computed from structural-signature embeddings · 2026-10-08