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Bondareva-Shapley

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  • Bruce C. Dieffenbach

    (Independent author)

Abstract

We study the core of a cooperative multi-person game with transferable utility. A payoff specifies the utility received by each player. By cooperating, a coalition of players can guarantee a certain utility—its worth—to be divided somehow among its members. The core is the set of payoffs such that no coalition can do better for itself. The worth of the grand coalition of all players is the value of the game. The primal models which payoffs are in the core. Furnishing the Bondareva-Shapley condition for the core to be non-empty, the dual finds the support to the “set of balanced weights,” evaluated at the worth. Whether the core is non-empty or empty is a matter of whether the support to the set of balanced weights evaluated at the worth equals the value or is greater, respectively.

Suggested Citation

  • Bruce C. Dieffenbach, 2026. "Bondareva-Shapley," Contributions to Economics,, Springer.
    • Handle: RePEc:spr:conchp:978-3-032-21396-9_51
    DOI: 10.1007/978-3-032-21396-9_51
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