The equity core and the Lorenz-maximal allocations in the equal division core

摘要

In this note, we give a geometrical decomposition of the equity core as a finite union of polyhedrons. As a consequence, we characterize the non-emptiness of the equity core (Selten in Decision theory and social ethics: issues in social choice, Reidel, Dordrecht, 289-301, 1978) and provide a method, easy to implement, for computing the Lorenz-maximal allocations in the equal division core (Dutta and Ray in Games Econ Behav 3:403-422, 1991).