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Novel auction schemes are constantly being designed. Their design hassignificant consequences for the allocation of goods and the revenuesgenerated. 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 ofthe Isabelle, Theorema, Mizar, and Hets/CASL/TPTP theorem provers forreproducing a key result of auction theory: Vickrey's 1961 theorem on theproperties of second-price auctions. Based on our formalisation experience,taking an auction designer's perspective, we give recommendations on whatsystem to use for formalising auctions, and outline further steps towards acomplete auction theory toolbox.

A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory