Egalitarian solutions in the core

In this paper we define the Lorenz stable set, a subset of the core consisting of the allocations that are not Lorenz dominated by any other allocation of the core. We introduce the leximin stable allocation, which is derived from the application of the Rawisian criterion on the core. We also define and axiomatize the egalitarian core, a set of core allocations for which no transfer from a rich player to a poor player is possible without violating the core restrictions. we find an inclusive relation of the leximin stable allocation and of the Lorenz stable set into the egalitarian core.