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

Christoph Lange, Marco B. Caminati, Manfred Kerber, Till Mossakowski, Colin Rowat, Makarius Wenzel, Wolfgang Windsteiger

In: Jacques Carette , James H. Davenport , Wolfgang Windsteiger , Petr Sojka , David Aspinall , Christoph Lange (Hrsg.). Conferences on Intelligent Computer Mathematics. Conferences on Intelligent Computer Mathematics (CICM-13) July 8-12 Bath United Kingdom Lecture Notes in Computer Science (LNCS) Springer 2013.


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.

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence