An Axiomatic Analysis of Interval Shapley Values

Interval games are an extension of cooperative coalitional games in which players are assumed to face payoff uncertainty as represented by a closed interval. In this study, we examine two interval-game versions of Shapley values (i.e., the interval Shapley value and the interval Shapley-like value), and characterize them using an axiomatic approach. For the interval Shapley value, we show that the existing axiomatization can be generalized to a wider subclass of interval games called size monotonic games. For the interval Shapley-like value, we show that a standard axiomatization using Young's strong monotonicity holds on the whole class of interval games