Aspects of Exchangeability in the Shapley Value

This paper characterizes the aspects of exchangeability in the Shapley value. We show that, in the Shapley value, each player’s prospects of joining a t-player game as the last member of the game is a moment sequence of the uniform distribution. We prove that, with finite exchangeability, the Shapley value is the only value in which the probability assignment is a unique mixture of independent and identically distributed probabilities. We also derive the Shapley value using the de Finetti’s theorem.