Abstract
We revisit the inefficiency of the uniform price auction, one of the standard multi-unit auction formats, for allocating multiple units of a single good. In the uniform price auction, each bidder submits a sequence of non-increasing marginal bids, one for each additional unit. The per unit price is then set to be the highest losing bid. We focus on the pure Nash equilibria of such auctions, for bidders with submodular valuation functions. Our result is a tight upper and lower bound on the inefficiency of equilibria, showing that the Price of Anarchy is bounded by 2.188. This resolves one of the open questions posed in previous works on multi-unit auctions.
This work has been partly supported by the University of Piraeus Research Center, and by a research program of the Athens University of Economics and Business.
This is a preview of subscription content, log in via an institution to check access.
Notes
- 1.
We note that Theorem 2 holds for any deterministic tie-breaking rule.
References
Ausubel, L., Cramton, P.: Demand reduction and inefficiency in multi-unit auctions. Techincal report, University of Maryland (2002)
Bhawalkar, K., Roughgarden, T.: Welfare guarantees for combinatorial auctions with item bidding. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 700–709 (2011)
Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. J. ACM 63(2), 11:1–11:19 (2016). (Preliminary version appeared at ICALP(1) 2008:820–832)
Christodoulou, G., Kovács, A., Sgouritsa, A., Tang, B.: Tight bounds for the price of anarchy of simultaneous first-price auctions. ACM Trans. Econ. Comput. 4(2), 9:1–9:33 (2016)
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)
Friedman, M.: A Program for Monetary Stability. Fordham University Press, New York (1960)
de Keijzer, B., Markakis, E., Schäfer, G., Telelis, O.: Inefficiency of standard multi-unit auctions. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 385–396. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40450-4_33. (Extended version available at arXiv:1303.1646)
Markakis, E., Telelis, O.: Uniform price auctions: equilibria and effciency. Theor. Comput. Syst. 57(3), 549–575 (2015). (Preliminary version appeared at SAGT2012:227–238)
Milgrom, P.: Putting Auction Theory to Work. Cambridge University Press, Cambridge (2004)
Ockenfels, A., Reiley, D.H., Sadrieh, A.: Economics and Information Systems. Handbooks in Information Systems, vol. 1, chap. 12, pp. 571–628. Online Auctions, Emerald Group Publishing Limited (2006)
Roughgarden, T.: Intrinsic robustness of the price of anarchy. J. ACM 62(5), 32:1–32:42 (2015). (Preliminary version appeared at ACM STOC 2009:513–522)
Syrgkanis, V., Tardos, E.: Composable and efficient mechanisms. In: Proceedings of the 45th ACM Symposium on the Theory of Computing (STOC 2013), pp. 211–220 (2013). (Extended version available at arXiv:1213.1325)
Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finan. 16(1), 8–37 (1961)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Birmpas, G., Markakis, E., Telelis, O., Tsikiridis, A. (2017). Tight Welfare Guarantees for Pure Nash Equilibria of the Uniform Price Auction. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-66700-3_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66699-0
Online ISBN: 978-3-319-66700-3
eBook Packages: Computer ScienceComputer Science (R0)