Kuhn's theorem

In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W.

Version

v1 · 2026-09-28 · History

Domain-specific #

10278

Domain group

Social Sciences

Origin domain

Economics & Finance

Subdomains

Game Theory, Extensive Form Games → Economics & Finance

Core Idea

Kuhn's theorem is treated here as the recurring game theory identity summarized by this source-grounded definition: In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W. In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W. The theorem establishes a formal equivalence between two types of strategies in extensive-form games with perfect recall: mixed strategies and behavior strategies.

Scope of Application

• Documented setting. This result ensures that behavior strategies—often simpler and more intuitive in sequential settings—can be used without loss of generality.

• Documented setting. In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W.

• Documented setting. The theorem establishes a formal equivalence between two types of strategies in extensive-form games with perfect recall: mixed strategies and behavior strategies.

• Documented setting. A mixed strategy assigns probabilities to complete plans of action (also called pure strategies), while a behavior strategy assigns probabilities to individual actions at each decision point.

• Documented setting. 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.

Clarity

A clear use of Kuhn's theorem names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W.

Manages Complexity

Kuhn's theorem compresses multiple game theory details into a stable diagnostic relation. The source shows both the central mechanism—the theorem establishes a formal equivalence between two types of strategies in extensive-form games with perfect recall: mixed strategies and behavior strategies.—and the practical consequence—the theorem plays a central role in simplifying the analysis of sequential games and underlies many results in both theoretical and applied game theory.

Abstract Reasoning

1. Type the carrier. Identify the game theory entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W.
3. Check operation and conditions. A mixed strategy assigns probabilities to complete plans of action (also called pure strategies), while a behavior strategy assigns probabilities to individual actions at each decision point.
4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Kuhn's theorem transfers literally when a new case preserves the same carrier type, relation, and recognition test. This result ensures that behavior strategies—often simpler and more intuitive in sequential settings—can be used without loss of generality. In game theory, Kuhn's theorem is a foundational result in the analysis of extensive-form games, first formalized by American mathematician Harold W. Beyond the home domain. No canonical parent is asserted for Kuhn's theorem.

Neighborhood in Abstraction Space

Kuhn's theorem sits in a sparse region of the domain-specific corpus (80^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Game-Theoretic Models & Paradoxes (37 abstractions)

Nearest neighbors

• Glicksberg's theorem — 0.83
• Bayes Correlated Equilibrium — 0.83
• Mixed Strategy Equilibrium — 0.83
• Strategy-stealing argument — 0.82
• One-shot deviation principle — 0.82

Computed from structural-signature embeddings · 2026-10-08