Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 40 / 4 / b / Solution

The Shapley value is the expected marginal contribution of a player when the players join in uniformly random order. Equivalently,For three players, the weights for predecessor sets of sizes $0,1,2$ are $1/3,1/6,1/3$. Using the computed values,Thus