A qualitative comparison of the suitability of four theorem provers for basic auction theory

Authors:
Christoph Lange;Marco B. Caminati;Manfred Kerber;Till Mossakowski;Colin Rowat;Makarius Wenzel;Wolfgang Windsteiger
Affiliations:
Computer Science, University of Birmingham, UK;-;Computer Science, University of Birmingham, UK;University of Bremen and DFKI GmbH Bremen, Germany;Economics, University of Birmingham, UK;Univ. Paris-Sud, Laboratoire LRI, Orsay, France;RISC, Johannes Kepler University Linz, Austria
Venue:
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
Year:
2013

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Abstract

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.