Characterization of Vickrey auction with reserve price for multiple objects

Abstract

This paper characterizes Vickrey auction with reserve price [VARP], in single and multiple objects settings, using normative and strategic axioms. In particular, it provides a new interpretation of reserve price as the infimum of a particular set of non-negative real numbers. In the single object case, we find that a strategyproof mechanism satisfies anonymity in welfare, agent sovereignty and non-bossiness in decision if and only if it has a VARP allocation rule. We extend this result to the multiple objects setting by introducing a continuity condition, and showing that any reasonable sale procedure (fixed prior to the realization of the number of available objects) involving continuous and strategyproof mechanisms that satisfy the aforementioned properties: must always use VARP with a fixed reserve price.