A Null-Player Axiom for the Myerson Value in Partition Function form Games: A Note

In this work, we explore solutions for partition function form games, where our basic approach is rooted in a concept of null player, derived directly from the carrier concept of Myerson [(1977) Int. J. Game Theory 6(1), 23-31]. We then show that the Myerson value cannot be characterized with the standard translation of Shapley's axioms of linearity, symmetry, efficiency and null-player to partition function form games. Instead, we provide an axiomatic characterization for the family of solutions for partition function form games satisfying those axioms, and we show that every such solution is a linear combination of specific marginal contributions of players.