Uncertainty of the Shapley Value
Vladislav Kargin
Abstract
This paper introduces a measure of uncertainty in the determination of the Shapley value, illustrates it with examples, and studies some of its properties. The introduced measure of uncertainty quantifies random variations in a player's marginal contribution during the bargaining process. The measure is symmetric with respect to exchangeable substitutions in the players, equal to zero for dummy player, and convex in the game argument. The measure is illustrated by several examples of abstract games and an example from epidemiology.
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