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Budget Imbalance Criteria for Auctions: A Formalized Theorem

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  • Marco B. Caminati
  • Manfred Kerber
  • Colin Rowat

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. "Budget Imbalance Criteria for Auctions: A Formalized Theorem," Papers 1412.0542, arXiv.org.
    • Handle: RePEc:arx:papers:1412.0542
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    References listed on IDEAS

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    1. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, June.
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