Bidding for the Surplus: a Non-Cooperative Approach to the Shapley Value. ation.

We consider zero-monotonic environments with transferable utility and propose a simple non-cooperative game to determine how the surplus generated by cooperation is to be shared. First, the players bid for the right to propose a sharing of the surplus. Second, after the winner pays the bids, she makes a proposal to each of the other players. If the proposal is rejected, the rest of the players will play the same game again with the proposer left out. If her proposal is accepted, she forms the grand coalition, keeping its value for herself in exchange for the proposed payments to the rest of the players. We show that the final outcome of any subgame perfect equilibrium of this mechanism always coincides with the vector of the Shapley value payoffs. Finally, we extend our results to implement the weighted Shapley values.