Potential, Value, and Consistency

Let P be a real-valued function defined on the space of cooperative games with transferable utility, satisfying the following condition: In every game, the marginal contributions of all players (according to P) are efficient (i.e., add up to the worth of the grand coalition). It is proved that there exists just one such function P--called the potential--and moreover that the resulting payoff vector coincides with the Shapley value. The potential approach yields other characterizations for the value; in particular, in terms of a new internal consistency property. Further results deal with weighted values and with the nontransferable utility case. Copyright 1989 by The Econometric Society.