Values for Environments with Externalities - The Average Approach

We propose the “average approach,” where the worth of a coalition is a weighted average of its worth for different partitions of the players’ set, as a unifying method to extend values for characteristic function form games. Our method allows us to extend the equal division value, the equal surplus value, the consensus value, the ë-egalitarian Shapley value, and the least-square family. For each of the first three extensions, we also provide an axiomatic characterization of a particular value for partition function form games. And for each of the last two extensions, we find a family of values that satisfy the properties.