Abstract
In a combinatorial auction, there are multiple items for sale, and bidders are allowed to place a bid on a bundle of these items rather than just on the individual items. A key problem in this and similar settings is that of strategic bidding, where bidders misreport their true preferences in order to effect a better outcome for themselves. The VCG payment scheme is the canonical method for motivating the bidders to bid truthfully. We study two related problems concerning the VCG payment scheme: the problem of revenue guarantees, and that of collusion. The existence of such problems is known by many; in this paper, we lay out their full extent.
We study four settings: combinatorial forward auctions with free disposal, combinatorial reverse auctions with free disposal, combinatorial forward (or reverse) auctions without free disposal, and combinatorial exchanges. In each setting, we give an example of how additional bidders (colluders) can make the outcome much worse (less revenue or higher cost) under the VCG payment scheme (but not under a first price scheme); derive necessary and sufficient conditions for such an effective collusion to be possible under the VCG payment scheme; and (when nontrivial) study the computational complexity of deciding whether these conditions hold.
This work is supported in part by NSF under CAREER Award IRI-9703122, Grant IIS-9800994, ITR IIS-0081246, and ITR IIS-0121678.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ausubel, L., Milgrom, P.: Ascending auctions with package bidding. Frontiers of Theoretical Economics 1(1), Article 1 (2002)
Bartal, Y., Gonen, R., Nisan, N.: Incentive compatible multi-unit combinatorial auctions. In: Theoretical Aspects of Rationality and Knowledge (TARK) (2003)
Clarke, E.H.: Multipart pricing of public goods. Public Choice 11, 17–33 (1971)
Conitzer, V., Sandholm, T.: Complexity of mechanism design. In: UAI (2002)
Conitzer, V., Sandholm, T.: Self-interested automated mechanism design and implications for optimal combinatorial auctions. In: ACM-EC (2004)
Gonen, R., Lehmann, D.: Optimal solutions for multi-unit combinatorial auctions: Branch and bound heuristics. In: ACM-EC (2000)
Green, J., Laffont, J.-J.: Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45, 427–438 (1977)
Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)
Lavi, R., Mu’Alem, A., Nisan, N.: Towards a characterization of truthful combinatorial auctions. In: FOCS (2003)
Lehmann, D., O’Callaghan, L.I., Shoham, Y.: Truth revelation in rapid, approximately efficient combinatorial auctions. JACM 49(5), 577–602 (2002)
Mas-Colell, A., Whinston, M., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)
Nisan, N.: Bidding and allocation in combinatorial auctions. In: ACM-EC (2000)
Nisan, N., Ronen, A.: Computationally feasible VCG mechanisms. In: ACM-EC (2000)
Parkes, D.: iBundle: An efficient ascending price bundle auction. In: ACM-EC (1999)
Rothkopf, M., Pekeč, A., Harstad, R.: Computationally manageable combinatorial auctions. Management Science 44(8), 1131–1147 (1998)
Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence 135, 1–54 (2002)
Sandholm, T., Suri, S., Gilpin, A., Levine, D.: CABOB: A fast optimal algorithm for combinatorial auctions. In: IJCAI (2001)
Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finance (1961)
Wurman, P., Wellman, M.: AkBA: A progressive, anonymous-price combinatorial auction. In: ACM-EC (2000)
Yokoo, M.: The characterization of strategy/false-name proof combinatorial auction protocols: Price-oriented, rationing-free protocol. In: IJCAI (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Conitzer, V., Sandholm, T. (2006). Revenue Failures and Collusion in Combinatorial Auctions and Exchanges with VCG Payments. In: Faratin, P., Rodríguez-Aguilar, J.A. (eds) Agent-Mediated Electronic Commerce VI. Theories for and Engineering of Distributed Mechanisms and Systems. AMEC 2004. Lecture Notes in Computer Science(), vol 3435. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11575726_1
Download citation
DOI: https://doi.org/10.1007/11575726_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29737-6
Online ISBN: 978-3-540-33166-7
eBook Packages: Computer ScienceComputer Science (R0)