Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set

New axiomatic characterizations of five classes of TU-values, the classes of the weighted, positively weighted, and multiweighted Shapley values, random order values, and the Harsanyi set are presented. Between all these well-known classes exists a real subset relationship. We combine axiomatizations of all individual classes into a single theorem or corollary for all classes at once. Thereby, the axiomatizations of two neighboring classes within a theorem or corollary differ by only one axiom, which is also known as parallel axiomatization or characterization. This gives us a deeper insight into the relationships between the classes. In conjunction with marginality, a new relaxation of mutual dependence (Nowak and Radzik, Games Econ Behav 8(2):389–405,1995), called coalitional differential dependence, is the key that allows us to dispense with additivity. Additionally, we propose new axiomatizations of the above five classes, in which different versions of monotonicity, associated with strong monotonicity, are decisive. Relaxations of superweak sign symmetry (Casajus, Econ Lett 176:75–78, 2019) allow the enlargement of solution classes to go hand in hand with the weakening of the changing axiom while the other axioms remain the same for all class axiomatizations.