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On the Shapley value of a minimum cost spanning tree problem

By Gustavo Bergantiños and Juan Vidal-Puga

Abstract

We associate an optimistic coalitional game with each minimum cost spanning tree problem. We define the worth of a coalition as the cost of connection assuming that the rest of the agents are already connected. We define a cost sharing rule as the Shapley value of this optimistic game. We prove that this rule coincides with a rule present in the literature under different names. We also introduce a new characterization using a property of equal contributions.minimum cost spanning tree problems Shapley value

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