A random assignment of indivisible goods in single-peaked economies with a common peak

Abstract

Bogomolnaia and Moulin (2001) show that there is no rule satisfying equal treatment of equals, sd-efficiency and sd-strategyproofness for a random assignment problem of indivisible goods. Furthermore, Kasajima (2013) shows that the incompatibility result holds when agents have single-peaked preferences. In this paper, we restrict the domain by requiring that all agents have a common peak and investigate the existence of rules satisfying the three axioms. We show that the three axioms are still incompatible. As it turns out, the three axioms are still incompatible even though all agents have the same preferences except the three least-preferable objects.