Efficient and strategy-proof allocation mechanisms in economies with many goods

Following the seminal work of Hurwicz (1972), the manipulability and efficiency of allocation mechanisms in pure exchange economies have been studied intensively. Zhou (1991) established that any Pareto-efficient and strategy-proof allocation mechanism is dictatorial in exchange economies with two agents having classical (i.e., continuous, strictly monotonic, and strictly convex) preferences. The dictatorship result in twoagent economies has been strengthened by being proven in the domain of restricted preferences.1 Compared with the result in two-agent economies, it is an open question whether Pareto-efficient and strategy-proof allocation mechanisms can be characterized in economies with many agents. This is the issue that we examine in this paper. In manyagent economies, there actually exist Pareto-efficient, strategy-proof, and nondictatorial allocation mechanisms. Satterthwaite and Sonnenschein (1981) constructed such a mechanism, relying on the reverse dictator’s preference, to select one agent among the remaining agents, who is allocated the total endowment. Kato and Ohseto (2002) constructed a mechanism in economies with four or more agents, such that all agents have the opportunity to be allocated the total endowment. A specific feature shared by all known Pareto-efficient and strategy-proof allocation mechanisms is that some single agent receives the whole amount of goods even if the receivers vary. Such a mechanism is called alternately dictatorial. The natural question to be asked is whether there exists a Pareto-efficient, strategy-proof, and nonalternately dictatorial allocation mechanism.