The Shapley value on convex geometries

https://doi.org/10.1016/S0166-218X(99)00218-8Get rights and content
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Abstract

A game on a convex geometry is a real-valued function defined on the family L of the closed sets of a closure operator which satisfies the finite Minkowski–Krein–Milman property. If L is the boolean algebra 2N then we obtain an n-person cooperative game. Faigle and Kern investigated games where L is the distributive lattice of the order ideals of the poset of players. We obtain two classes of axioms that give rise to a unique Shapley value for games on convex geometries.

Keywords

Cooperative game
Convex geometry
Shapley value

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