Walrasian Pricing in Multi-Unit Auctions

Authors Simina Brânzei, Aris Filos-Ratsikas, Peter Bro Miltersen, Yulong Zeng

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Simina Brânzei
Aris Filos-Ratsikas
Peter Bro Miltersen
Yulong Zeng

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Simina Brânzei, Aris Filos-Ratsikas, Peter Bro Miltersen, and Yulong Zeng. Walrasian Pricing in Multi-Unit Auctions. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 80:1-80:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Multi-unit auctions are a paradigmatic model, where a seller brings multiple units of a good, while several buyers bring monetary endowments. It is well known that Walrasian equilibria do not always exist in this model, however compelling relaxations such as Walrasian envy-free pricing do. In this paper we design an optimal envy-free mechanism for multi-unit auctions with budgets. When the market is even mildly competitive, the approximation ratios of this mechanism are small constants for both the revenue and welfare objectives, and in fact for welfare the approximation converges to 1 as the market becomes fully competitive. We also give an impossibility theorem, showing that truthfulness requires discarding resources, and in particular, is incompatible with (Pareto) efficiency.
  • mechanism design
  • multi-unit auctions
  • Walrasian pricing
  • market share


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