Shapley's Theorem characterizes the Shapley value, a way of dividing the total payoff of a cooperative game among its players, as the unique division satisfying four axioms: efficiency, meaning the whole payoff is distributed; symmetry, meaning interchangeable players receive equal shares; the null player property, meaning a player contributing nothing receives nothing; and additivity across combined games. Named for Lloyd Shapley, it gives the Shapley value its standard axiomatic justification as a fair allocation rule in cooperative game theory.
Facts
StatementThe Shapley value is the only division of a cooperative game's payoff that satisfies efficiency, symmetry, additivity, and the dummy (null) player property. 1 Classification
Statement FormCharacterization 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 Shapley value (Wikipedia)
Sources
1. Shapley value (Wikipedia)
Introduction, sentence on four properties
It is the only solution that satisfies four fundamental properties: efficiency, symmetry, additivity, and the dummy player (or null player) property
Introduction, sentence on naming
It was named in honor of Lloyd Shapley, who introduced it in 1951.
In Branch: Game Theory, Lead sentence
In cooperative game theory, the Shapley value is a method (solution concept) for fairly distributing the total gains or costs amon
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