Approximately-strategyproof and tractable multi-unit auctions

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multi-unit allocation problem. The bidding language in our auctions allows marginal-decreasing piecewise constant curves. First, we develop a fully polynomial-time approximation scheme for the multi-unit allocation problem, which computes a (1+ε)≈ in worst-case time T = O(n3/ε), given n bids each with a constant number of pieces. Second, we embed this approximation scheme within a Vickrey-Clarke-Groves (VCG) mechanism and compute payments to n agents for an asymptotic cost of O(T log n). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by ε/(1+ε) V, where V is the total surplus in the efficient outcome.

[1]  Y. Shoham,et al.  Truth revelation in rapid, approximately efficient combinatorial auctions , 2001 .

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

[3]  David C. Parkes,et al.  Auction design with costly preference elicitation , 2005, Annals of Mathematics and Artificial Intelligence.

[4]  Gabriel Y. Weintraub,et al.  A Combinational Auction Improves School Meals in Chile , 2002, Interfaces.

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

[6]  Oscar H. Ibarra,et al.  Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.

[7]  Eugene Levner,et al.  Computational Complexity of Approximation Algorithms for Combinatorial Problems , 1979, MFCS.

[8]  Éva Tardos,et al.  An approximate truthful mechanism for combinatorial auctions with single parameter agents , 2003, SODA '03.

[9]  Soumyadip Ghosh,et al.  Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves , 2005, J. Heuristics.

[10]  Yoav Shoham,et al.  Truth revelation in approximately efficient combinatorial auctions , 2002, EC '99.

[11]  Joan Feigenbaum,et al.  Distributed algorithmic mechanism design: recent results and future directions , 2002, DIALM '02.

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

[13]  Lawrence M. Ausubel,et al.  The Optimality of Being Efficient , 1999 .

[14]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

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

[16]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[17]  Tuomas Sandholm,et al.  Algorithm for optimal winner determination in combinatorial auctions , 2002, Artif. Intell..

[18]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[19]  Harry R. Lewis.  Review: Michael R. Garey, David S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness , 1983 .

[20]  J. Håstad.  Clique is hard to approximate withinn1−ε , 1999 .

[21]  Peter Cramton,et al.  Vickrey auctions with reserve pricing , 2004 .

[22]  Makoto Yokoo,et al.  The effect of false-name bids in combinatorial auctions: new fraud in internet auctions , 2004, Games Econ. Behav..

[23]  Linus Schrage,et al.  An Auction Method for Course Registration , 1993 .

[24]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[25]  Sven de Vries,et al.  Linear Programming and Vickrey Auctions , 2001 .

[26]  David S. L. Wei,et al.  Computer Algorithms , 1998, Scalable Computing : Practice and Experience.

[27]  Hans Kellerer,et al.  Approximation algorithms for knapsack problems with cardinality constraints , 2000, Eur. J. Oper. Res..

[28]  Ho Soo Lee,et al.  Computational Aspects of Clearing Continuous Call Double Auctions with Assignment Constraints and Indivisible Demand , 2001, Electron. Commer. Res..

[29]  Vijay Krishna,et al.  Efficient Mechanism Design , 1998 .

[30]  Kalyan Chatterjee,et al.  Bargaining under Incomplete Information , 1983, Oper. Res..

[31]  David C. Parkes,et al.  Achieving Budget-Balance with Vickrey-Based Payment Schemes in Exchanges , 2001, IJCAI.

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

[33]  J. Schummer.  Almost-dominant Strategy Implementation , 1999 .

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

[35]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

[36]  Michael P. Wellman,et al.  Auction Protocols for Decentralized Scheduling , 2001, Games Econ. Behav..

[37]  Michael P. Wellman,et al.  Combinatorial auctions for supply chain formation , 2000, EC '00.

[38]  Joseph A. Swanson,et al.  Special Issue: Experimental Economics in Practice: The First Use of a Combined-Value Auction for Transportation Services , 2002, Interfaces.

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

[40]  Makoto Yokoo,et al.  A robust open ascending-price multi-unit auction protocol against false-name bids , 2003, EC '03.

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

[42]  J. Håstad.  Clique is hard to approximate within n 1-C , 1996 .

[43]  Noam Nisan,et al.  Towards a characterization of truthful combinatorial auctions , 2003, 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings..

[44]  Jakka Sairamesh,et al.  Profit-Driven Matching in E-Marketplaces: Trading Composable Commodities , 1999, Agent Mediated Electronic Commerce.