Multilinear Extensions of Games

The multilinear extension of an n-person game v is a function defined on the n-cube I^N which is linear in each variable and which coincides with v at the conrners of the cube, satisfying f(x) = v({i ∣ x_i = 1}). Multilinear extensions are useful as a help in computing the values of large games, and give a generalization of the Shapley value.