  Novel auction schemes are constantly being designed. Their design has
significant consequences for the allocation of goods and the revenues
generated. But how to tell whether a new design has the desired properties,
such as efficiency, i.e. allocating goods to those bidders who value them most?
We say: by formal, machine-checked proofs. We investigated the suitability of
the Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers for
reproducing a key result of auction theory: Vickrey's 1961 theorem on the
properties of second-price auctions. Based on our formalisation experience,
taking an auction designer's perspective, we give recommendations on what
system to use for formalising auctions, and outline further steps towards a
complete auction theory toolbox.
