Bidding for the surplus: A non-cooperative approach to the Shapley value

We propose a simple mechanism to determine how the surplus generated by coo peration is to be shared in zero-monotonic environments with transferable u tility. The mechanism consists of a bidding stage followed by a proposal st age. We show that the subgame perfect equilibrium outcomes of this mechanis m coincide with the vector of the Shapley value payoffs, We extend our resu lts to implement the weighted Shapley values. Finally, we generalize our me chanism to handle arbitrary transferable utility environments. The modified mechanism generates an efficient coalition structure, and implements the S hapley values of the superadditive cover of the environment. (C) 2001 Acade mic Press.