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.
This work has been supported by EPSRC grant EP/J007498/1. We would like to thank Peter Cramton and Elizabeth Baldwin for sharing their auction designer’s point, and Christian Maeder for his recent improvements to Hets.
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Lange, C. et al. (2013). A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds) Intelligent Computer Mathematics. CICM 2013. Lecture Notes in Computer Science(), vol 7961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39320-4_13
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DOI: https://doi.org/10.1007/978-3-642-39320-4_13
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