Potential and Consistency: A Uniform Approach to Values for TU-Games

摘要

A value on the set G of all transferable utility games is said to have apotential representation if there exists a potential function P G approaches real numbers such that, for any player in any game, his appropriately chosen incremental contribution with respect to the potential agrees with his value in the game. The main theorem states that a value has a potential representation if and only if the value has a potential representation if and only if the value satisfies the classical efficiency, linearity and symmetry axioms, together with two additional conditions involving a collection of constants which describe such a value. For the general class of values which have a potential representation, it is further established that such a value possesses the consistency property with respect to an appropriately chosen type of reduced game. Finally, an axiomatic characterization of any value which has a potential representation is given in terms of two axioms, namely the corresponding consistency axiom together with an axiom referring to some kind of standardness for two-person games.