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

We propose a simple mechanism to determine how the surplus generated by cooperation is to be shared in zero-monotonic environments with transferable utility. The mechanism consists of a bidding stage followed by a proposal stage. We show that the subgame perfect equilibrium outcomes of this mechanism coincide with the vector of the Shapley value payoffs, We extend our results to implement the weighted Shapley values. Finally, we generalize our mechanism to handle arbitrary transferable utility environments. The modified mechanism generates an efficient coalition structure, and implements the Shapley values of the superadditive cover of the environment. (C) 2001 Academic Press.