Weighted Potential and Consistency: A Unified Approach to Values for TU-Games211 (Revised Version)

摘要

A value on the set G of all transferable utility games is said to have a weighted211u001epotential representation if there exists a potential function P : G -> R, 211u001eassociated with a collection of weights, such that, for every game and every 211u001eplayer, an appropriately chosen weighted extension of the player's marginal 211u001econtribution (with respect to the potential) agrees with the player's value in 211u001ethe game. The main theorem states that a value has a weighted potential 211u001erepresentation if and only if the value satisfies the well-known efficiency, 211u001elinearity and symmetry axioms, together with two additional conditions involving 211u001ea unique collection of constants that describes such a value. Particularly, this 211u001eunified approach provides various weighted potential representations for the 211u001eShapley value, the solidarity value as well and several egalitarian values based 211u001eon some kind of equity principle.