Shapley value of a coverage game (${\varphi }_i(v)={\sum }_{b\in B_i}|\{j:b\in B_j\}{|}^{-1}$)

Decompose a coverage coalitional game into one-resource games and use additivity of the Shapley value. A player contributes a resource precisely when it is the earliest player in a random ordering among those holding that resource. Each holder has probability the reciprocal of the number of holders of being earliest. Summing these contributions proves the formula, regardless of overlaps or emptiness of the core.