Balanced externalities and the Shapley value

Abstract

We characterize the Shapley value using (together with standard conditions of efficiency and equal gains in two-player games) a condition of ‘undominated merge-externalities’. Similar to the well-known ‘balanced contributions’ characterization, our characterization corresponds intuitively to ‘threat points’ present in bargaining. It derives from the observation that all semivalues satisfy ‘balanced merge-externalities’. Our characterization is applicable to useful, narrow sub-classes of games (including monotonic simple games), and also extends naturally to encompass games in partition function form.