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Uniform Price Auctions: Equilibria and Efficiency

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Abstract

We study the Uniform Price Auction, one of the standard sealed-bid multi-unit auction formats in Auction Theory, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is generally inefficient, due to a “Demand Reduction” effect; bidders tend to bid for fewer (identical) units, so as to receive them at a lower uniform price. All the same, the uniform pricing rule is popular by its appeal to the anticipation that identical items should be identically priced. Its applications include, among others, sales of U.S. Treasury notes to investors and trade exchanges over the Internet facilitated by popular online brokers. In this work, we characterize pure undominated bidding strategies and give an algorithm for computing pure Nash equilibria in such strategies. Subsequently we show that their Price of Anarchy is \(\frac {e}{e-1}\). Finally, we show that the Price of Anarchy of mixed Bayes-Nash equilibria with undominated support is at most \(4-\frac {2}{k}\), where k is the number of auctioned items. To the best of our knowledge, our work provides the first (constructive) proof of existence of pure Nash equilibria in undominated strategies and the first performance evaluation (with respect to economic efficiency) of this popular auction format.

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Notes

  1. Among them, eBay ceased its own variant in 2009.

  2. It is known that for submodular valuation functions on identical units, the allocation algorithm of the Uniform Price Auction produces an optimal allocation when bidders bid truthfully. This property does not hold in the case of non-identical items, where only a 2-approximation is achieved [17].

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Acknowledgements

This work has been supported by the research project “DDCOD” (PE6-213). The project is implemented within the framework of the Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. Evangelos Markakis also acknowledges support by the project ”THALES-AGT”, which is cofinanced by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program ”Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) Research Funding Program: THALES.

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  1. Department of Informatics, Athens University of Economics and Business, Patision 76, 10434, Athens, Greece

    Evangelos Markakis & Orestis Telelis

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  1. Evangelos Markakis
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  2. Orestis Telelis
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Correspondence to Orestis Telelis.

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A preliminary version appeared in Proceedings of the 5th International Symposium on Algorithmic Game Theory (SAGT 2012) [20].

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Markakis, E., Telelis, O. Uniform Price Auctions: Equilibria and Efficiency. Theory Comput Syst 57, 549–575 (2015). https://doi.org/10.1007/s00224-014-9537-9

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