NO-ENVY AND CONSISTENCY IN ECONOMIES WITH INDIVISIBLE GOODS

We consider the problem of fair allocation in economies with indivisible goods. Our main objective is to identify appealing subsolutions of the no-envy solution. We formulate desirable properties of solutions, and look for solutions satisfying them: given an allocation chosen by a solution for some economy and given a subgroup of the agents, consider the problem of fairly distributing among its members the resources that this group has collectively received. The solution is consistent if it recommends that the same bundle be attributed to each of these agents as initially. We show that there is no proper subsolution of the no-envy solution that satisfies consistency. However, many subsolutions satisfy bilateral consistency or the converse of consistency. But again, there is no proper subsolution satisfying these two properties together.