An Ascending-Price Generalized Vickrey Auction

A simple characterization of the equilibrium conditions required to compute Vickrey payments in the Combinatorial Allocation Problem leads to an ascending price Generalized Vickrey Auction. The ascending auction, iBundle Extend & Adjust (iBEA), maintains non-linear and perhaps non-anonymous prices on bundles of items, and terminates with the efficient allocation and the Vickrey payments in ex post Nash equilibrium. Crucially, iBEA is able to implement the Vickrey outcome even when the Vickrey payments are not supported in a single competitive equilibrium. The auction closes with Universal competitive equilibrium prices, which provide enough information to compute individualized discounts to adjust the final prices and implement Vickrey payments.

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

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

[3]  G. Nemhauser,et al.  Integer Programming , 2020 .

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

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

[6]  C. d'Aspremont,et al.  Incentives and incomplete information , 1979 .

[7]  K. Arrow.  The Property Rights Doctrine and Demand Revelation under Incomplete Information**This work was supported by National Science Foundation under Grant No. SOC75-21820 at the Institute for Mathematical Studies in the Social Sciences, Stanford University. , 1979 .

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

[9]  V. Crawford,et al.  Job Matching with Heterogeneous Firms and Workers , 1981 .

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

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

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

[13]  H. Leonard.  Elicitation of Honest Preferences for the Assignment of Individuals to Positions , 1983, Journal of Political Economy.

[14]  D. Gale,et al.  Multi-Item Auctions , 1986, Journal of Political Economy.

[15]  J. Banks,et al.  Allocating uncertain and unresponsive resources: an experimental approach. , 1989, The Rand journal of economics.

[16]  Dimitri P. Bertsekas,et al.  The Auction Algorithm for Assignment and Other Network Flow Problems: A Tutorial , 1990 .

[17]  M. Rothkopf,et al.  Why Are Vickrey Auctions Rare? , 1990, Journal of Political Economy.

[18]  Tuomas Sandholm,et al.  An Implementation of the Contract Net Protocol Based on Marginal Cost Calculations , 1993, AAAI.

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

[20]  J. Mcmillan.  Selling Spectrum Rights , 1994 .

[21]  J. Ledyard,et al.  The allocation of a shared resource within an organization , 1996 .

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

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

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

[25]  David C. Parkes,et al.  iBundle: an efficient ascending price bundle auction , 1999, EC '99.

[26]  David C. Parkes,et al.  Optimal Auction Design for Agents with Hard Valuation Problems , 1999, Agent Mediated Electronic Commerce.

[27]  J. Ledyard,et al.  A NEW AND IMPROVED DESIGN FOR MULTI-OBJECT ITERATIVE AUCTIONS , 1999 .

[28]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[29]  Lawrence M. Ausubel,et al.  From single static to multiple dynamic combinatorial auctions , 2005, ACM International Conference on International Agent Technology.

[30]  David C. Parkes,et al.  Preventing Strategic Manipulation in Iterative Auctions: Proxy Agents and Price-Adjustment , 2000, AAAI/IAAI.

[31]  Michael P. Wellman,et al.  AkBA: a progressive, anonymous-price combinatorial auction , 2000, EC '00.

[32]  Ennio Stacchetti,et al.  The English Auction with Differentiated Commodities , 2000, J. Econ. Theory.

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

[34]  P. Jehiel.  On the virtues of the ascending price auction : New insights in the private value setting , 2000 .

[35]  Leandro Arozamena,et al.  Investment Incentives in Procurement Auctions , 2000 .

[36]  Noam Nisan,et al.  Computationally feasible VCG mechanisms , 2000, EC '00.

[37]  Vol Cxv Issue.  EFFICIENT AUCTIONS , 2000 .

[38]  Paul R. Milgrom,et al.  Putting Auction Theory to Work: The Simultaneous Ascending Auction , 1999, Journal of Political Economy.

[39]  Mark M. Bykowsky,et al.  Mutually Destructive Bidding: The FCC Auction Design Problem , 2000 .

[40]  Luke Hunsberger,et al.  A combinatorial auction for collaborative planning , 2000, Proceedings Fourth International Conference on MultiAgent Systems.

[41]  B. Moldovanu,et al.  The European Umts/Imt-2000 Licence Auctions , 2001 .

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

[43]  David C. Parkes,et al.  An Iterative Generalized Vickrey Auction: Strategy-Proofness without Complete Revelation , 2001 .

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

[45]  David C. Parkes,et al.  Iterative combinatorial auctions: achieving economic and computational efficiency , 2001 .

[46]  Daniel Lehmann,et al.  Combinatorial auctions with decreasing marginal utilities , 2001, EC '01.

[47]  Noam Nisan,et al.  An efficient approximate allocation algorithm for combinatorial auctions , 2001, EC '01.

[48]  David Levine,et al.  CABOB: A Fast Optimal Algorithm for Combinatorial Auctions , 2001, IJCAI.

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

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

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

[52]  Lawrence M. Ausubel.  An Efficient Ascending-Bid Auction for Multiple Objects , 2004 .