An Axiomatization of the Shapley Mapping Using Strong Monotonicity in Interval Games

Abstract

Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty. Characteristic functions thus assign a closed interval instead of a real number. In this paper, we focus on interval game versions of Shapley values. First, we modify Young's strong monotonicity axiom for coalitional games into two versions so that they can be applied to the Shapley mapping and show that this can be axiomatized within the entire class of interval games using either version. Second, we derive the Shapley mapping for specific examples by employing two approaches used in the proof of the axiomatization and argue that our approach is more effective than existing methods in terms of addressing the subtraction operator problem inherent to interval game analyses.

Keywords: cooperative interval games, interval uncertainty, Shapley value, Shapley mapping, Interval Shapley value, axiomatization, strong monotonicity