The egalitarian solution for the class of convex TU games was defined by Dutta and Ray [1989] and axiomatized by Dutta 1990. An extension of this solution — the egalitarian split-off set (ESOS) — to the class of non-levelled NTU games is proposed. On the class of TU games it coincides with the egalitarian split-off set [Branzei et al. 2006]. The proposed extension is axiomatized as the maximal (w.r.t. inclusion) solution satisfying consistency à la Hart–Mas-Colell and agreeing with the solution of constrained egalitarianism for arbitrary two-person games. For ordinal convex NTU games the ESOS turns out to be single-valued and contained in the core. The totally cardinal convexity property of NTU games is defined. For the class of ordinal and total cardinal convex NTU games an axiomatic characterization of the Dutta–Ray solution with the help of Peleg consistency is given.
Two new axioms, additivity of additional bonus (AAB) and reduced game monotonicity (RGM), are introduced. AAB states that the players can gain an additional bonus after they achieved an agreement; on the other hand, if the bargaining fails then they get nothing. With its help, we characterise the lexicographic egalitarian solution by individual rationality (IR), AAB and consistency (CON). The other axiom, RGM, is a weaker axiom than CON and strong monotonicity (SMON), respectively. Using Pareto optimal (PO), IR, AAB and RGM, the second characterisation of the lexicographic egalitarian solution is presented.
Fairness in Multiterminal Data Compression: A Splitting Method for the Egalitarian Solution