Locally efficient and strategy-proof allocation mechanisms in exchange economies

In this paper, we investigate whether efficiency and strategy-proofness of allocation mechanisms defined on a “local” preference set imply dictatorship. Although there is an extensive literature on the characterization of efficient and strategy-proof allocation mechanisms defined on the whole preference set, little attention has been given to a local characterization even in two-agent economies. This paper presents three results. First, we point out that locally efficient, strategy-proof, and nondictatorial allocation mechanisms exists even in two-agent economies, when boundary allocations can be efficient. Second, excluding such exceptional cases, we show that in economies where the number of goods equals or exceeds the number of agents, any efficient and strategy-proof allocation mechanism defined on any local preference domain is alternately dictatorial, that is, it always allocates the total amount of goods to some single agent, even if the receivers vary. Third, we clarify that the local characterization is generally an open question even with allocation conditions such as the minimum consumption guarantee, and show that efficiency and strategy-proofness are incompatible with allocation conditions when all agents have the same local preference set.