Abstract
Our main goal is to abstract existing repeated sponsored search ad auction mechanisms which includes budgets, and study their equilibrium and dynamics. Our abstraction has multiple agents biding repeatedly for multiple identical items (such as impressions in an ad auction). The agents are budget limited and have a value for per item. We abstract the repeated interaction as a one-shot game, which we call budget auction, where agents submit a bid and a budget, and then items are sold by a sequential second price auction. Once an agent exhausts its budget it does not participate in the proceeding auctions.
Our main result is that if agents bid conservatively (never bid above their value) then there always exists a pure Nash equilibrium. We also study simple dynamics of repeated budget auctions, showing their convergence to a Nash equilibrium for two agents and for multiple agents with identical budgets.
This research was supported in part by the Google Inter-university center for Electronic Markets and Auctions, by a grant from the Israel Science Foundation, by a grant from United States-Israel Binational Science Foundation (BSF), and by a grant from the Israeli Ministry of Science (MoS).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Andelman, N., Mansour, Y.: Auctions with budget constraints. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 26–38. Springer, Heidelberg (2004)
Asdemir, K.: Bidding patterns in search engine auctions. In: In Second Workshop on Sponsored Search Auctions, ACM Electronic Commerce, Press (2006)
Azar, Y., Birnbaum, B.E., Karlin, A.R., Mathieu, C., Nguyen, C.T.: Improved approximation algorithms for budgeted allocations. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 186–197. Springer, Heidelberg (2008)
Azar, Y., Birnbaum, B.E., Karlin, A.R., Nguyen, C.T.: On revenue maximization in second-price ad auctions. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 155–166. Springer, Heidelberg (2009)
Babaioff, M., Sharma, Y., Slivkins, A.: Characterizing truthful multi-armed bandit mechanisms: extended abstract. In: ACM Conference on Electronic Commerce, pp. 79–88 (2009)
Bhawalkar, K., Roughgarden, T.: Welfare guarantees for combinatorial auctions with item bidding. In: SODA (2011)
Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: EC 2005: Proceedings of the 6th ACM Conference on Electronic Commerce, pp. 44–51 (2005)
Borgs, C., Immorlica, N., Chayes, J., Jain, K.: Dynamics of bid optimization in online advertisement auctions. In: Proceedings of the 16th International World Wide Web Conference, pp. 13–723 (2007)
Cary, M., Das, A., Edelman, B., Giotis, I., Heimerl, K., Karlin, A.R., Mathieu, C., Schwarz, M.: Greedy bidding strategies for keyword auctions. In: ACM Conference on Electronic Commerce, pp. 262–271 (2007)
Devanur, N.R., Kakade, S.M.: The price of truthfulness for pay-per-click auctions. In: ACM Conference on Electronic Commerce, pp. 99–106 (2009)
Dobzinski, S., Nisan, N., Lavi, R.: Multi-unit auctions with budget limits. In: Proc. of the 49th Annual Symposium on Foundations of Computer Science, FOCS (2008)
Edelman, B., Ostrovsky, M.: Strategic bidder behavior in sponsored search auctions. In: Workshop on Sponsored Search Auctions, ACM Electronic Commerce, pp. 192–198 (2005)
Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second price auction: Selling billions of dollars worth of keywords. American Economic Review 97 (2005)
Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: ACM Conference on Electronic Commerce 2011, pp. 223–232 (2011)
Kitts, B., LeBlanc, B.J.: Optimal bidding on keyword auctions. Electronic Markets 14(3), 186–201 (2004)
Leme, R.P., Tardos, É.: Pure and bayes-nash price of anarchy for generalized second price auction. In: FOCS, pp. 735–744 (2010)
Markakis, E., Telelis, O.: Discrete strategies in keyword auctions and their inefficiency for locally aware bidders. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 523–530. Springer, Heidelberg (2010)
Mehta, A., Saberi, A., Vazirani, U., Vazirani, V.: Adwords and generalized online matching. J. ACM 54(5), 22 (2007)
Muthukrishnan, S.: Ad exchanges: Research issues. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 1–12. Springer, Heidelberg (2009)
Nisan, N.: Google’s auction for TV ads. In: Fiat, A., Sanders, P. (eds.) ESA 2009. LNCS, vol. 5757, pp. 553–553. Springer, Heidelberg (2009)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.: Algorithmic Game Theory, Cambridge (2007)
Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Trans. Netw. 1(5), 510–521 (1993)
Varian, H.R.: Position auctions. International Journal of Industrial Organization (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Arnon, A., Mansour, Y. (2011). Repeated Budgeted Second Price Ad Auction. In: Persiano, G. (eds) Algorithmic Game Theory. SAGT 2011. Lecture Notes in Computer Science, vol 6982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24829-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-24829-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24828-3
Online ISBN: 978-3-642-24829-0
eBook Packages: Computer ScienceComputer Science (R0)