Two Characterisations of the Lexicographic egalitarian Solution

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.