Strategy-proofness in linear production economies with homothetic or quasi-linear preferences

In an economy with linear production, under a richness condition on the domain of preferences, efficiency, equal treatment of equals, and strategy-proofness are compatible. We characterize the rules satisfying the three properties. They are “equal-income Walrasian rules”, selections from the equal-income Walrasian correspondence. Important domains of preferences (e.g. homothetic preferences and quasi-linear preferences) satisfy the condition. These domains are important, yet they are not covered by Maniquet and Sprumont (Econ. Theory 14(3):583–595, 1999) who characterize the same family of rules on a different domain. Our condition and theirs are logically independent.