Strategy-Proof and Efficient Allocation of an Indivisible Good on Finitely Restricted Preference Domains

We consider allocation mechanisms in economies with a single indivisible good and money. First, we show that there is no strategy-proof and Pareto efficient mechanism on some preference domains which consist of a sufficiently large but finite number of quasi-linear preferences. Second, we show that there is no strategy-proof, Pareto efficient, and equally compensatory mechanism on arbitrary preference domains which consist of more than three quasi-linear preferences. Key words: Strategy-proofness, efficiency, domain restriction