Abstract
Auctions like sponsored search often implicitly or explicitly require that bidders are treated fairly. This may be because large bidders have market power to negotiate equal treatment, because small bidders are difficult to identify, or for many other reasons. We study so-called anonymous auctions to understand the revenue tradeoffs and to develop simple anonymous auctions that are approximately optimal.
We begin with the canonical digital goods setting and show that the optimal anonymous, ex-post incentive compatible auction has an intuitive structure — imagine that bidders are randomly permuted before the auction, then infer a posterior belief about bidder i’s valuation from the values of other bidders and set a posted price that maximizes revenue given this posterior.
We prove that no anonymous mechanism can guarantee an approximation better than \(\varTheta (n)\) to the optimal revenue in the worst case (or \(\varTheta (\log n)\) for regular distributions) and that even posted price mechanisms match those guarantees. Understanding that the real power of anonymous mechanisms comes when the auctioneer can infer the bidder identities accurately, we show a tight \(\varTheta (k)\) approximation guarantee when each bidder can be confused with at most k “higher types”. Moreover, we introduce a simple mechanism based on n target prices that is asymptotically optimal. Finally, we return to our original motivation and build on this mechanism to extend our results to m-unit auctions and sponsored search.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In some sense, the search engine would like to set a reserve price for the top slot. However, this must be carefully defined when no bidder meets the reserve price or when more than one bidder meets it; the decreasing price mechanism we discuss later in this paper may be considered a natural interpretation of setting different reserve prices for different slots in a sponsored search auction.
- 2.
Many factors, such as click-through-rates (CTRs) and relevance scores, will break symmetry in a sponsored search auction. As discussed in Ashlagi [3], these can be handled in a variety of ways, e.g. by requiring symmetry among bidders with the same CTR or score. We follow Ashlagi and consider a simple model without such parameters to avoid these complexities.
- 3.
Truthful reporting by the agents can be made an ex-post Nash Equilibrium by canceling the auction completely if an agent misreported his identity and the mechanism receives an identity twice.
- 4.
This is a regular VCG mechanism with a reserve price p.
References
Alaei, S., Hartline, J.D., Niazadeh, R., Pountourakis, E., Yuan, Y.: Optimal auctions vs. anonymous pricing. In: Guruswami, V. (ed.) IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, Berkeley, CA, USA, 17–20 October 2015, pp. 1446–1463. IEEE Computer Society (2015)
Archer, A., Tardos, É.: Truthful mechanisms for one-parameter agents. In: FOCS 2001: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, p. 482. IEEE Computer Society, Washington, DC (2001)
Ashlagi, I.: A characterization of anonymous truth-revealing position auctions. Harvard University, Discussion Paper, Harvard Business School (2008)
Azar, P.D., Daskalakis, C., Micali, S., Weinberg, S.M.: Optimal and efficient parametric auctions. In: SODA, pp. 596–604 (2013)
Balcan, M.-F., Blum, A., Mansour, Y.: Item pricing for revenue maximization. In: Proceedings of the 9th ACM conference on Electronic commerce, pp. 50–59. ACM (2008)
Cremer, J., McLean, R.P.: Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica 53(2), 345–361 (1985)
Deb, R., Pai, M.: Discrimination via symmetric auctions. Am. Econ. J. Microecon. (2015)
Dhangwatnotai, P., Roughgarden, T., Yan, Q.: Revenue maximization with a single sample. In: Proceedings of the 11th ACM Conference on Electronic Commerce, EC 2010, pp. 129–138. ACM, New York (2010)
Feldman, M., Fiat, A., Leonardi, S., Sankowski, P.: Revenue maximizing envy-free multi-unit auctions with budgets. In: Proceedings of the 13th ACM Conference on Electronic Commerce, pp. 532–549. ACM (2012)
Goldberg, A.V., Hartline, J.D.: Envy-free auctions for digital goods. In: Proceedings of the 4th ACM Conference on Electronic Commerce, pp. 29–35. ACM (2003)
Guruswami, V., Hartline, J.D., Karlin, A.R., Kempe, D., Kenyon, C., McSherry, F.: On profit-maximizing envy-free pricing. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1164–1173. Society for Industrial and Applied Mathematics (2005)
Hartline, J.D., Roughgarden, T.: Simple versus optimal mechanisms. SIGecom Exch. 8(1), 5:1–5:3 (2009)
Myerson, R.B.: Optimal auction design. Math. Oper. Res. 6(1), 58–73 (1981)
Ronen, A.: On approximating optimal auctions. In: Proceedings of the 3rd ACM Conference on Electronic Commerce, pp. 11–17. ACM (2001)
Roughgarden, T., Talgam-Cohen, I.: Optimal and near-optimal mechanism design with interdependent values. In: Proceedings of the Fourteenth ACM Conference on Electronic Commerce, EC 2013, pp. 767–784. ACM, New York (2013)
Segal, I.: Optimal pricing mechanisms with unknown demand. Am. Econ. Rev. 93(3), 509–529 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag GmbH Germany
About this paper
Cite this paper
Tzamos, C., Wilkens, C.A. (2016). Anonymous Auctions Maximizing Revenue. In: Cai, Y., Vetta, A. (eds) Web and Internet Economics. WINE 2016. Lecture Notes in Computer Science(), vol 10123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-54110-4_14
Download citation
DOI: https://doi.org/10.1007/978-3-662-54110-4_14
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-54109-8
Online ISBN: 978-3-662-54110-4
eBook Packages: Computer ScienceComputer Science (R0)