Abstract
In this paper the model of multi-choice games on matroids is defined. The explicit expression of a Shapley function for the given multi-choice games is presented. Meantime, characterizations of the given Shapley function are discussed. Two of which are inspired by Shapley's axioms for the Shapley function in traditional case; others are enlightened by Young's characterizations for the Shapley function in classical case. When multi-choice games on matroids are convex, the relationship between the core, its subcore and the Shapley function is researched. Finally, a numerical example is given.
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