The Bondareva-Shapley Theorem characterizes when the core of a cooperative game with transferable payoffs is nonempty, meaning some way of dividing the grand coalition's total value leaves no smaller coalition better off acting alone, showing this holds exactly when the game is balanced in a precise technical sense. Named for Olga Bondareva and Lloyd Shapley, who proved it independently, it is a foundational existence result of cooperative game theory.
Facts
StatementThe core of a cooperative game with transferable payoffs is non-empty if and only if the game is balanced. 2 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.
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Source Bondareva-Shapley theorem - Wikipedia
Sources
1. Wikipedia: Bondareva-Shapley theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Specifically, the game's core is non-empty if and only if the game is balanced.
2. Bondareva-Shapley theorem - Wikipedia
Theorem section
The game's core is non-empty if and only if the game is balanced.
References section
Bondareva, Olga N. (1963). Some applications of linear programming methods to the theory of cooperative games (In Russian). Problemy Kybernetiki.
- In Branch: Game Theory, Lead sentence
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