Potential, Value, and Consistency

Sergiu Hart and Andreu Mas-Colell

(Acrobat PDF file)

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 the Shapley value. The potential approach is also shown to yield other characterizations for the Shapley value, in particular, in terms of a new internal consistency property. Further results deal with weighted Shapley values (which emerge from the above consistency) and with the nontransferable utility case (where the egalitarian solutions and the Harsanyi value are obtained).