Implementing egalitarian-equivalent allocation of indivisible goods on restricted domains

We study the problem of allocating several units of homogeneous indivisible goods when monetary compensations are possible. First, we show that there is no strategy-proof, budget balanced, and egalitarian-equivalent mechanism even on extremely restricted preference domains. Next, we present two characterizations of strategy-proof and decision-efficient mechanisms that satisfy a stronger version of egalitarian-equivalence on preference domains bounded above. These characterizations tell us a trade-off between strategy-proofness and Pareto efficiency, and a relationship with strategy-proof and envy-free mechanisms. Finally, we prove that no egalitarian-equivalent mechanism is Nash implementable even on extremely restricted preference domains.