The Pareto Dominant Strategy-Proof and Equitable Rule for Problems with Indivisible Goods

We study the problem of allocating indivisible goods to agents when monetary compensations are not allowed. Our central requirements are strategy-proofness and equity. For each of two different cases of this problem we identify a strategy-proof and equitable [in the sense of equal-treatment-of-equals, or envy-freeness] rule that Pareto dominates all other equitable and strategy-proof rules.