<p>This paper investigates (non-)manipulability properties of Walrasian equilibrium rules in object allocation problems with non-quasi-linear preferences. We focus on assignment problems with indivisible and different objects where each agent is interested in acquiring at most one object. We propose simplified forms of manipulation such as reporting a monotonic transformation of preferences or pretending to be single-minded.</p><p>We show that the minimum Walrasian equilibrium rule is the unique rule that, among all Walrasian equilibrium rules, is non-manipulable via monotonic transformations at the outside option. 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.</p><p>Finally, on the domain of quasi-linear preferences, we introduce a novel axiom: welfare parity for uncontested objects. Under this axiom, when a new object, valued positively by only one agent, enters the market, that agent receives all the resulting welfare gain. We prove that, within this domain, the axiom characterizes the minimum Walrasian equilibrium rule among all Walrasian equilibrium rules.</p>