An equivalent formulation for the Shapley value

The final authenticated version is available online at: https://doi.org/10.1007/978-3-662-58464-4_1.An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.Peer ReviewedPostprint (published version