Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: May, 1989, Volume 57, Issue 3

Potential, Value, and Consistency<589:PVAC>2.0.CO;2-S
p. 589-614

Andreu Mas-Colell, Sergiu Hart

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 exist just one such function P--called the potential--and moreover that the resulting payoff vector coincides with 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).

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