Combinatorial Auctions: Complexity and Algorithms

In the following, we provide an overview of complexity inherent in the design of combinatorial auctions, and discuss how these challenges are addressed in various combinatorial auction formats. A combinatorial auction allows bidders to submit bids on bundles of objects and can be considered the pivotal example of a multiple object auctions. They also constitute a paradigmatic problem in algorithmic mechanism design. We provide an overview of both the computational complexity and strategic complexity inherent in the design of such auctions, and discuss how these challenges are addressed in various combinatorial auction formats. Keywords: combinatorial auction; computational complexity; strategic complexity; VCG mechanism

[1]  Sven de Vries,et al.  Combinatorial Auctions: A Survey , 2003, INFORMS J. Comput..

[2]  David C. Parkes,et al.  Ascending Price Vickrey Auctions for General Valuations , 2005, J. Econ. Theory.

[3]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[4]  Lawrence M. Ausubel,et al.  The Clock-Proxy Auction: A Practical Combinatorial Auction Design , 2004 .

[5]  Chris Caplice,et al.  Combinatorial Auctions for Truckload Transportation , 2005 .

[6]  Sven de Vries,et al.  On ascending Vickrey auctions for heterogeneous objects , 2007, J. Econ. Theory.

[7]  Ronnie Belmans,et al.  Block order restrictions in combinatorial electric energy auctions , 2009, Eur. J. Oper. Res..

[8]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[9]  Martin Bichler,et al.  Configurable offers and winner determination in multi-attribute auctions , 2005, Eur. J. Oper. Res..

[10]  Sushil Bikhchandani,et al.  The Package Assignment Model , 2002, J. Econ. Theory.

[11]  Anthony M. Kwasnica,et al.  A New and Improved Design for Multiobject Iterative Auctions , 2005, Manag. Sci..

[12]  Dries R. Goossens,et al.  Exact algorithms for procurement problems under a total quantity discount structure , 2007, Eur. J. Oper. Res..

[13]  Lawrence M. Ausubel,et al.  The Lovely but Lonely Vickrey Auction , 2004 .

[14]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[15]  David Porter,et al.  Combinatorial auction design , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Jerry R. Green,et al.  Characterization of Satisfactory Mechanisms for the Revelation of Preferences for Public Goods , 1977 .

[17]  Yoav Shoham,et al.  Empirical hardness models: Methodology and a case study on combinatorial auctions , 2009, JACM.

[18]  S. Rassenti,et al.  A Combinatorial Auction Mechanism for Airport Time Slot Allocation , 1982 .

[19]  K. Arrow,et al.  EXISTENCE OF AN EQUILIBRIUM FOR A COMPETITIVE ECONOMY , 1954 .

[20]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[21]  Martin Bichler,et al.  Industrial Procurement Auctions , 2005 .

[22]  Ronald M. Harstad,et al.  Computationally Manageable Combinational Auctions , 1998 .

[23]  Charles A. Holt,et al.  An Experimental Test of Flexible Combinatorial Spectrum Auction Formats , 2010 .

[24]  Rudolf Müller,et al.  Tractable cases of the winner determination problem , 2006 .

[25]  Paul Milgrom,et al.  Core-selecting package auctions , 2008, Int. J. Game Theory.

[26]  E. Maasland,et al.  Auction Theory , 2021, Springer Texts in Business and Economics.

[27]  S. Reiter,et al.  The informational size of message spaces , 1974 .

[28]  F. Kelly,et al.  A Combinatorial Auction with Multiple Winners for Universal Service , 2000 .

[29]  D. Lehmann,et al.  The Winner Determination Problem , 2003 .

[30]  Noam Nisan,et al.  The communication requirements of efficient allocations and supporting prices , 2006, J. Econ. Theory.

[31]  A. Adam.  Whatever happened to information systems ethics? Caught between the devil and the deep blue sea , 2004 .

[32]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[33]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[34]  Ron Lavi,et al.  Algorithmic Mechanism Design , 2008, Encyclopedia of Algorithms.

[35]  R. McAfee,et al.  Auctions and Bidding , 1986 .

[36]  Martin Bichler,et al.  An Experimental Comparison of Linear and Nonlinear Price Combinatorial Auctions , 2011, Inf. Syst. Res..

[37]  Jacob K. Goeree,et al.  Hierarchical package bidding: A paper & pencil combinatorial auction , 2010, Games Econ. Behav..

[38]  Lawrence M. Ausubel,et al.  Ascending Proxy Auctions , 2005 .

[39]  Martin Bichler,et al.  A Computational Analysis of Linear Price Iterative Combinatorial Auction Formats , 2009, Inf. Syst. Res..

[40]  Martin Bichler,et al.  On the robustness of non-linear personalized price combinatorial auctions , 2010, Eur. J. Oper. Res..

[41]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[42]  Andrew J. Davenport,et al.  Price Negotiations for Procurement of Direct Inputs , 2002 .

[43]  S. Bikhchandani,et al.  Competitive Equilibrium in an Exchange Economy with Indivisibilities , 1997 .

[44]  Alok Gupta,et al.  Toward Comprehensive Real-Time Bidder Support in Iterative Combinatorial Auctions , 2005, Inf. Syst. Res..

[45]  David C. Parkes,et al.  Iterative Combinatorial Auctions , 2006 .

[46]  Michael H. Rothkopf,et al.  Thirteen Reasons Why the Vickrey-Clarke-Groves Process Is Not Practical , 2007, Oper. Res..

[47]  Tuomas Sandholm,et al.  Approaches to winner determination in combinatorial auctions , 2000, Decis. Support Syst..

[48]  P. Klemperer.  Auction Theory: A Guide to the Literature , 1999 .

[49]  Rudolf Müller,et al.  Optimization in electronic markets: examples in combinatorial auctions , 2001 .

[50]  David C. Parkes,et al.  Iterative Combinatorial Auctions: Theory and Practice , 2000, AAAI/IAAI.

[51]  Martin Pesendorfer,et al.  Auctioning bus routes: the London experience , 2006 .