Note on social choice allocation in exchange economies with many agents

We show that in pure exchange economies there exists no Pareto-efficient and strategy-proof allocation mechanism that ensures positive consumption for all agents. We also show that a Pareto-efficient, strategy-proof, and non-bossy allocation mechanism is dictatorial. We further show that in three-agent economies, the allocation given by a Pareto-efficient, strategy-proof, and non-dictatorial mechanism depends only on one agentʼs preference who is always allocated zero consumption. That is, in three-agent economies, Zhouʼs (1991) [14] conjecture is true and any Pareto-efficient and strategy-proof mechanism is of Satterthwaite and Sonnenscheinʼs (1981) [10] type.