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arXiv · 1412.0542

Budget Imbalance Criteria for Auctions: A Formalized Theorem

Marco B. Caminati·Manfred Kerber·Colin Rowat
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Abstract

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 constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such a sum is not constant. In particular, this theorem applies to the important case of a second-price Vickrey auction, where it reduces to a basic result of which a novel proof is given. To enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are re- produced here in common mathematical language, and are accompanied by an informal discussion about the underlying ideas.

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Marco B. Caminati, Manfred Kerber, Colin Rowat. 2014-11-07. Budget Imbalance Criteria for Auctions: A Formalized Theorem. https://arxiv.org/abs/1412.0542

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