Monotonic transformation of preferences and Walrasian equilibrium in allocation problems

Abstract

This paper investigates (non-)manipulability properties and welfare effects of Walrasian equilibrium rules in object allocation problems with non-quasi-linear preferences. We focus on allocation problems with indivisible and different objects. The agents are interested in acquiring at most one object. We show that the minimum Walrasian equilibrium rule is the unique rule that is non-manipulable via monotonic transformations at the outside option among the set of Walrasian equilibrium rules. Analogously, we also show that the minimum Walrasian equilibrium rule is also the unique Walrasian equilibrium rule that is non-manipulable by pretending to be single-minded. On the domain of quasi-linear preferences, we introduce a novel axiom: welfare parity for uncontested objects. On this domain, this axiom is enough to characterize the minimum Walrasian equilibrium rule among the set of Walrasian equilibrium rules.