No-Envy and Consistency in Economies with Indivisible Goods.

The authors study fair allocation in economies with indivisible goods. They look for subsolutions of the no-envy solution satisfying the property of consistency which says that the desirability of an allocation for some economy is unaffected by the departure of some of the agents with their allotted bundles. The authors show that essentially there is no proper subsolution of the no-envy solution satisfying consistency. However, many subsolutions satisfy a bilateral version of the condition and many satisfy its converse. But again, there is essentially no proper subsolution satisfying bilateral consistency and converse consistency together. Copyright 1991 by The Econometric Society.