Strategy-Proof Multidimensional Mechanism Design

We consider direct mechanisms to sell heterogeneous objects when buyers have private additive valuations and nonunit demand. We completely characterize the class of strategy-proof and agent sovereign mechanisms that satisfy a local side-flatness condition. Further, we introduce a notion of “continuity up to utility” and show that any such mechanism allocating all objects at all profiles is continuous and anonymous only if it is efficient. We find that the only mechanism satisfying these properties is equivalent to operating simultaneous second-price auctions for each object—as was done by the New Zealand government in allocating license rights to the use of radio spectrum in 1990. Finally, we present a complete characterization of simultaneous second-price auctions with object-specific reserve prices in terms of these properties and a weak nonbossiness restriction.