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Theory of Computing Systems

, Volume 59, Issue 1, pp 1–23 | Cite as

On the Stability of Generalized Second Price Auctions with Budgets

  • Josep Díaz
  • Ioannis Giotis
  • Lefteris Kirousis
  • Evangelos Markakis
  • Maria Serna
Article
  • 159 Downloads

Abstract

The Generalized Second Price (GSP) auction used typically to model sponsored search auctions does not include the notion of budget constraints, which is present in practice. Motivated by this, we introduce the different variants of GSP auctions that take budgets into account in natural ways. We examine their stability by focusing on the existence of Nash equilibria and envy-free assignments. We highlight the differences between these mechanisms and find that only some of them exhibit both notions of stability. This shows the importance of carefully picking the right mechanism to ensure stable outcomes in the presence of budgets.

Keywords

Auctions Second price Sponsored search Keyword auctions 

Notes

Acknowledgements

We would like to thank Konstantinos Gavriil for pointing out to us the counterexample of Fig. 2, that without distinct budgets, envy-free assignments may fail to exist. We also want to thank Giorgos Birbas for valuable discussions during the preparation of this work.

This research has also been co-financed 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. Investing in knowledge society through the European Social Fund.

Josep Díaz, Maria J. Serna and Ioannis Giotis supported by the CICYT project TIN-2007-66523 (FORMALISM).

References

  1. 1.
    Arnon, A., Mansour, Y. Repeated budgeted second price ad auction. Theory of Computing Systems pp. 1–26 (2013). doi: 10.1007/s00224-013-9472-1
  2. 2.
    Ashlagi, I., Braverman, M., Hassidim, A., Lavi, R., Tennenholtz, M.: Position auctions with budgets: existence and uniqueness. B.E, Journal of Theoretical Economics Advances (to appear) (2013)Google Scholar
  3. 3.
    Ausubel, L.M.: An efficient ascending-bid auction for multiple objects. Am. Econ. Rev. 94(5), 1452–1475 (2004)CrossRefGoogle Scholar
  4. 4.
    Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: ACM Conference on Electronic Commerce (EC), pp 44–51 (2005)Google Scholar
  5. 5.
    Caragiannis, I., Kaklamanis, K., Kanellopoulos, P., Kyropoulou, M., Lucier, B., Paes Leme, R., Tardos, E.: On the efficiency of equilibria in generalized second price auctions. arXiv:1201.6429 (2012)
  6. 6.
    Chakrabarty, D., Zhou, Y., Lukose, R.: Budget constrained bidding in keyword auctions and online knapsack problems. In: Workshop on Internet and Network Economics (WINE), pp 566–576 (2008)Google Scholar
  7. 7.
    Charles, D., Chakrabarty, D., Chickering, M., Devanur, N.R., Wang, L.: Budget smoothing for internet ad auctions: a game theoretic approach. In: Proceedings of the fourteenth ACM conference on Electronic commerce, pp 163–180. EC ’13, ACM, NY, USA (2013). doi: 10.1145/2482540.2482583
  8. 8.
    Christodoulou, G., Kovács, A., Schapira, M.: Bayesian combinatorial auctions. In: ICALP (1), pp 820–832 (2008)Google Scholar
  9. 9.
    Colini-Baldeschi, R., Henzinger, M., Leonardi, S., Starnberger, M.: On multiple keyword sponsored search auctions with budgets. In: Czumaj, A., Mehlhorn, K., Pitts, A.M., Wattenhofer, R. (eds.) Automata, Languages, and Programming - 39th International Colloquium, ICALP 2012. Lecture Notes in Computer Science, vol. 7392, pp 1–12. Springer (2012)Google Scholar
  10. 10.
    Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. In: Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science, pp 260–269. FOCS ’08, IEEE Computer Society, DC, USA (2008). doi: 10.1109/FOCS.2008.39
  11. 11.
    Edelman, B., Ostrovsky, M.: Strategic bidder behavior in sponsored search auctions. Decis. Support. Syst. 43, 192–198 (2007)CrossRefGoogle Scholar
  12. 12.
    Edelman, B., Ostrovsky, M., Schwarz, M.: Internet advertising and the generalized second-price auction: Selling billions of dollars worth of keywords. Am. Econ. Rev. 97(1), 242–259 (2007)CrossRefGoogle Scholar
  13. 13.
    Feldman, J., Muthukrishnan, S., Pal, M., Stein, C.: Budget optimization in search-based advertising auctions. In: ACM Conference on Electronic Commerce (EC), pp 40–49 (2007)Google Scholar
  14. 14.
    Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: Proceedings of the 12th ACM conference on Electronic commerce, pp 223–232. EC ’11, ACM, NY, USA (2011). doi: 10.1145/1993574.1993609
  15. 15.
    Goel, G., Mirrokni, V.S., Leme, R.P.: Polyhedral clinching auctions and the adwords polytope. In: ACM Symposium on Theory of Computing (STOC), pp 107–122 (2012)Google Scholar
  16. 16.
    Lahaie, S., Pennock, D., Saberi, A., Vohra, R.: Sponsored search auctions. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory, pp 699–716. Cambridge University Press (2007)Google Scholar
  17. 17.
    Lahaie, S., Pennock, D.: Revenue analysis of a family of ranking rules for keyword auctions, pp 50–56. Proceedings ACM Conference on Electronic Commerce (EC), California, USA (2007)Google Scholar
  18. 18.
    Maillé, P., Markakis, E., Naldi, M., Stamoulis, G.D., Tuffin, B.: Sponsored search auctions: an overview of research with emphasis on game theoretic aspects. Electron. Commer. Res. 12(3), 265–300 (2012)CrossRefGoogle Scholar
  19. 19.
    Syrgkanis, V., Tardos, É.: Composable and efficient mechanisms. In: ACM Symposium on Theory of Computing (STOC 2013), pp 211–220 (2013)Google Scholar
  20. 20.
    Varian, H.: Position auctions. Int. J. Ind. Organ. 25, 1163–1178 (2005)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Josep Díaz
    • 1
  • Ioannis Giotis
    • 1
  • Lefteris Kirousis
    • 2
    • 3
  • Evangelos Markakis
    • 4
  • Maria Serna
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformaticsUniversitat Politecnica de CatalunyaBarcelonaSpain
  2. 2.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  3. 3.Computer Technology Institute and Press “Diophantus”AthensGreece
  4. 4.Department of InformaticsAthens University of Economics and BusinessAthensGreece

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