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

@article{Lange2013AQC, title={A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory}, author={Christoph Lange and Marco B. Caminati and Manfred Kerber and Till Mossakowski and Colin Rowat and Markus Wenzel and Wolfgang Windsteiger}, journal={ArXiv}, year={2013}, volume={abs/1303.4193} }

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…

## 19 Citations

Budget Imbalance Criteria for Auctions: A Formalized Theorem

- Computer Science, MathematicsArXiv
- 2014

We present an original theorem in auction theory: it specifies general conditions under which the sum of the payments of all bidders is necessarily not identically zero, and more generally not…

Sound Auction Specification and Implementation

- Computer ScienceEC
- 2015

We introduce `formal methods' of mechanized reasoning from computer science to address two problems in auction design and practice: is a given auction design soundly specified, possessing its…

Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?

- Computer ScienceCICM
- 2014

Three of the theorems from Maskin’s 2004 survey article on Auction Theory are proved using the Isabelle/HOL system, and software code that implements combinatorial Vickrey auctions is verified.

The Formalization of Vickrey Auctions: A Comparison of Two Approaches in Isabelle and Theorema

- MathematicsCICM
- 2017

A complete formalization of Vickrey’s Theorem in Theorema 2.0 with the original formalization in Isabelle is compared and an overview on statistical indicators, such as number of auxiliary lemmas and the total number of proof steps needed for all proofs in the theory is given.

Formally Verified Trades in Financial Markets

- Economics, Computer ScienceICFEM
- 2020

This paper introduces a formal framework for analyzing trades in financial markets and uses this framework to verify properties of two important classes of double sided auction mechanisms.

Formal verification of trading in financial markets

- Economics, Computer ScienceArXiv
- 2019

This paper introduces a formal framework for analyzing trades in financial markets and uses this framework to verify properties of two important classes of double sided auctions.

Proving soundness of combinatorial Vickrey auctions and generating verified executable code

- Computer Science, EconomicsArXiv
- 2013

Using mechanised reasoning it is proved that combinatorial Vickrey auctions are soundly specified in that they associate a unique outcome to any valid input and auto-generate verified executable code from the formally defined auction.

A Formal Proof of Vickrey's Theorem by Blast, Simp, and Rule

- Economics, Mathematics
- 2014

This paper applies formal methods to a familiar environment - Vickrey's theorem on second-price auctions - and provides, as background, an introduction to formal methods.

University of Birmingham Sound auction specification and implementation

- Computer Science
- 2015

Sound auction specification and implementation 2015, and its implementation in EC '15 Proceedings of the Sixteenth ACM Conference on Economics and Computation.

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