On a new method of analyzing properties of efficient, symmetric and linear values of TU-games

We present a new method allowing one to discover different extra properties of efficient, symmetric and linear values of TU-games (called ESL-values). These properties are of “monotonicity”, “acceptability” and “null player properties” type. A representation formula for such family of values, generalizing the standard formula for the Shapley value, is recalled. It is then shown that a number of different properties of ESL-values can be easily identified using this formula. Several new axiomatizations of different ESL-values are also obtained as simple consequences of the presented theorems. A table of different properties for fifteen basic ESL-values is given as an illustration of the new method.