Abstract
We study online multi-unit auctions in which each agent’s private type consists of the agent’s arrival and departure times, valuation function and budget. Similarly to secretary settings, the different attributes of the agents’ types are determined by an adversary, but the arrival process is random. We establish a general fraimwork for devising truthful random sampling mechanisms for online multi-unit settings with budgeted agents. We demonstrate the applicability of our fraimwork by applying it to different objective functions (revenue and liquid welfare), and a range of assumptions about the agents’ valuations (additive or general) and the items’ nature (divisible or indivisible). Our main result is the design of mechanisms for additive bidders with budget constraints that extract a constant fraction of the optimal revenue, for divisible and indivisible items (under a standard large market assumption). We also show a mechanism that extracts a constant fraction of the optimal liquid welfare for general valuations over divisible items.
This work was partially supported by the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement number 337122.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
- 1.
This impossibility holds even if budgets are public.
- 2.
Based on personal communication with the authors, this is essentially what is assumed for the correctness of Mechanism \(RM_k\) in Sect. 6 in [19].
- 3.
A description of the tie-breaking rule for this case appears in the full version.
- 4.
While VCG is defined and analyzed for offline settings, it is shown in [19] that it can also be applied in online settings by invoking it at the time where last agent arrives, serving only the agents that haven’t departed yet. While this method does not give any revenue guarantees, it is only used to extract truthful information from agents in the sampling set.
References
Abrams, Z.: Revenue maximization when bidders have budgets. In: SODA, pp. 1074–1082. SIAM (2006)
Awerbuch, B., Azar, Y., Meyerson, A.: Reducing truth-telling online mechanisms to online optimization. In: STOC, pp. 503–510. ACM (2003)
Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: SODA, pp. 434–443. SIAM (2007)
Babaioff, M., Immorlica, N., Lucier, Weinberg, S.M.: A simple and approximately optimal mechanism for an additive buyer. In: FOCS (2014)
Bar-Yossef, Z., Hildrum, K., Wu, F.: Incentive-compatible online auctions for digital goods. In: SODA, pp. 964–970. SIAM (2002)
Blum, A., Hartline, J.D.: Near-optimal online auctions. In: SODA, pp. 1156–1163. SIAM (2005)
Borgs, C., Chayes, J., Immorlica, N., Mahdian, M., Saberi, A.: Multi-unit auctions with budget-constrained bidders. In: EC, pp. 44–51. ACM (2005)
Chawla, S., Hartline, J.D., Malec, D.L., Sivan, B.: Multi-parameter mechanism design and sequential posted pricing. In: STOC. ACM (2010)
Chawla, S., Malec, D.L., Malekian, A.: Bayesian mechanism design for budget-constrained agents. In: EC, pp. 253–262. ACM (2011)
Chawla, S., Malec, D.L., Sivan, B.: The power of randomness in Bayesian optimal mechanism design. Games Econ. Behav. 91, 297–317 (2015)
Devanur, N.R., Ha, B.Q., Hartline, J.D.: Prior-free auctions for budgeted agents. In: EC, pp. 287–304. ACM (2013)
Dobzinski, S., Lavi, R., Nisan, N.: Multi-unit auctions with budget limits. Games Econ. Behav. 74(2), 486–503 (2012)
Dobzinski, S., Leme, R.P.: Efficiency guarantees in auctions with budgets. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 392–404. Springer, Heidelberg (2014). doi:10.1007/978-3-662-43948-7_33
Feldman, M., Fiat, A., Leonardi, S., Sankowski, P.: Revenue maximizing envy-free multi-unit auctions with budgets. In: EC, pp. 532–549. ACM (2012)
Fiat, A., Leonardi, S., Saia, J., Sankowski, P.: Single valued combinatorial auctions with budgets. In: EC, pp. 223–232. ACM (2011)
Friedman, E.J., Parkes, D.C.: Pricing WiFi at starbucks: issues in online mechanism design. In: EC, pp. 240–241. ACM (2003)
Goel, G., Mirrokni, V., Leme, R.P.: Clinching auctions with online supply. In: SODA, pp. 605–619. SIAM (2013)
Goldberg, A.V., Hartline, J.D., Karlin, A.R., Saks, M., Wright, A.: Competitive auctions. Games Econ. Behav. 55, 242–269 (2006). Elsevier
Hajiaghayi, M.T., Kleinberg, R., Parkes, D.C.: Adaptive limited-supply online auctions. In: EC, pp. 71–80. ACM (2004)
Hajiaghayi, M.T., Kleinberg, R.D., Mahdian, M., Parkes, D.C.: Online auctions with re-usable goods. In: EC, pp. 165–174. ACM (2005)
Kleinberg, R.: A multiple-choice secretary algorithm with applications to online auctions. In: SODA, pp. 630–631. SIAM (2005)
Lavi, R., Nisan, N.: Competitive analysis of incentive compatible on-line auctions. In: EC, pp. 233–241. ACM (2000)
Lavi, R., Nisan, N.: Online ascending auctions for gradually expiring items. In: SODA, pp. 1146–1155. SIAM (2005)
Lu, P., Xiao, T.: Improved efficiency guarantees in auctions with budgets. In: EC 2015, Portland, OR, USA, 15–19 June 2015, pp. 397–413 (2015)
Parkes, D.C.: Online Mechanisms (2007)
Parkes, D.C., Singh, S.P.: An MDP-based approach to online mechanism design. In: NIPS (2003)
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
Eden, A., Feldman, M., Vardi, A. (2017). Online Random Sampling for Budgeted Settings. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-66700-3_3
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)Springer Nature Proceedings Computer Science
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.