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

  title={The equity core and the Lorenz-maximal allocations in the equal division core},
  author={Francesc Llerena and Cori Vilella},
  journal={Mathematical Methods of Operations Research},
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). 
1 Citations

The equity core and the core

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