On Axioms Underlying Use of Reserve Price

This paper establishes reserve price as an ethical necessity contrary to its popular interpretation as an instrument of revenue generation. It provides an axiomatic justification to reserve pricing at Vickrey auction in single as well as multiple objects settings. It also provides a multi-object axiomatization of another popular class reserve price mechanisms called maxmed mechanisms introduced by Sprumont [JET,2013]. In general, a topological interpretation of reserve price is provided as the infimum of the set of non-negative real numbers satisfying the following property: if all agents bid the same number from this set, then at least one object is allocated. For the single object setting, (i) it is shown that any anonymous strategy-proof mechanism that satisfies non-bossiness (in decision) must have an allocation rule same as that of a Vickrey auction with reserve price (VARP) and (ii) an axiomatization is provided for the class of VARP mechanisms. The same results are shown to hold in multiple objects context under an additional ethical axiom minimal impartiality (which requires that either all objects or no object be allocated at any profile where all agents report the same value) and a technical regularity condition. These results are further extended to provide a characterization of maxmed mechanisms in the multiple object setting.