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Kuhn's Theorem

Game Theory

Kuhn's Theorem states that in an extensive-form game with perfect recall, meaning every player always remembers their own past moves and information, mixed strategies and behavioral strategies are equivalent in the sense of producing the same distribution over outcomes. Named for Harold Kuhn, it justifies the common practice of analyzing such games using the simpler behavioral-strategy framework, in which a player randomizes independently at each information set, without loss of generality.

Facts
Statement
In a finite extensive-form game with perfect recall, every mixed strategy has an equivalent behavior strategy yielding the same outcome probabilities, and vice versa. 1
Proof Year
1953 1
Classification
Statement Form
Characterization Theorem 1
Connections

Has Statement Form

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

In Branch

Source Kuhn's theorem (Wikipedia)
Sources
1. Kuhn's theorem (Wikipedia)
  • Introduction, statement sentence
    Kuhn's theorem shows that in any finite extensive-form game where players have perfect recall (the ability to remember all of their previous moves and information), every mixed strategy has an equivalent behavior strategy that yields the same outcome probabilities, and vice versa.
  • Introduction, sentence on formalization
    first formalized by American mathematician Harold W. Kuhn in 1953
  • In Branch: Game Theory, Lead sentence
    In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American math
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