We explore the relationship between non-manipulability via merging (splitting) and strong non-manipulability via merging (splitting). We show that although, in general, these non-manipulability properties are not equivalent, under the principle of solidarity, fulfilled by a wide range of...

We show that on the domain of convex games, Dutta-Ray's egalitarian solution is characterized by core selection, aggregate monotonicity, and bounded richness, a new property requiring that the poorest players cannot be made richer within the core. Replacing "poorest" by "poorer" allows to...