Potential, Value, and Consistency
Sergiu Hart and Andreu Mas-Colell
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).
Econometrica 57 (1989), 3, 589-614