Note on social choice allocation in exchange economies with many agents

In this paper we show that in pure exchange economies there exists no Pareto efficient and strategy-proof allocation mechanism which ensures positive consumptions to all agents. We also show that Pareto efficient, strategy-proof, and non-bossy allocation mechanism is dictatorial. We further show that if there exists three agents, then the allocation given by a Pareto efficient, strategy-proof, and non-dictatorial mechanism should depend only on one consumer’s preference who is always allocated zero consumption. That is, we prove Zhou’s (1991) conjecture in three-agent economies and show that a Pareto efficient and strategy-proof social choice function in such an economy should be Satterthwaite and Sonnenschein’s (1981) type. JEL classification: , .