On the Computational Power of Iterative Auctions I: Demand Queries

We study the computational power and limitations of iterative combinatorial auctions. Most existing iterative combinatorial auctions are based on repeatedly suggesting prices for bundles of items, and querying the bidders for their ``demand'' under these prices. We prove several results regarding such auctions that use a polynomial number of demand queries: (1) that such auctions can simulate several other natural types of queries; (2) that such auctions can solve linear programming relaxations of winner determination problems; (3) that they can approximate the optimal allocation as well as generally possible using polynomial communication or computation, while weaker types of queries can not do so. We also initiate the study of how can the prices of bundles be represented when they are not linear, and show that the ``default'' representation has severe limitations.

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

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

[3]  Johan Håstad,et al.  Almost optimal lower bounds for small depth circuits , 1986, STOC '86.

[4]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

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

[6]  Noam Nisan,et al.  Bidding and allocation in combinatorial auctions , 2000, EC '00.

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

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

[9]  N. Nisan.  The Communication Complexity of Approximate Set Packing and Covering , 2002, ICALP.

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

[11]  David C. Parkes,et al.  An Ascending-Price Generalized Vickrey Auction , 2002 .

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

[13]  Noam Nisany,et al.  The Communication Requirements of E¢cient Allocations and Supporting Lindahl Prices¤ , 2003 .

[14]  Avrim Blum,et al.  Preference Elicitation and Query Learning , 2004, J. Mach. Learn. Res..

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

[16]  David C. Parkes,et al.  Applying learning algorithms to preference elicitation , 2004, EC '04.

[17]  Moshe Tennenholtz,et al.  Bundling equilibrium in combinatorial auctions , 2002, Games Econ. Behav..

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

[19]  Berthold Vöcking,et al.  Approximation techniques for utilitarian mechanism design , 2005, STOC '05.

[20]  Noam Nisan,et al.  Exponential communication inefficiency of demand queries , 2005, TARK.

[21]  Shahar Dobzinski,et al.  Approximation algorithms for cas with complement - free bidders , 2005 .

[22]  N. Nisan,et al.  On the Computational Power of Iterative Auctions II: Ascending Auctions , 2005 .

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

[24]  Moshe Babaioff,et al.  Combinatorial agency , 2006, EC '06.

[25]  Uriel Feige,et al.  On maximizing welfare when utility functions are subadditive , 2006, STOC '06.

[26]  Shahar Dobzinski,et al.  An improved approximation algorithm for combinatorial auctions with submodular bidders , 2006, SODA '06.

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

[28]  Lawrence M. Ausubel.  An efficient dynamic auction for heterogeneous commodities , 2006 .

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

[30]  Shahar Dobzinski,et al.  Welfare Maximization in Congestion Games , 2006, IEEE Journal on Selected Areas in Communications.

[31]  Yuval Rabani,et al.  Linear Programming , 2007, Handbook of Approximation Algorithms and Metaheuristics.

[32]  Ilya Segal,et al.  The communication requirements of social choice rules and supporting budget sets , 2007, J. Econ. Theory.

[33]  Michel Gendreau,et al.  Combinatorial auctions , 2007, Ann. Oper. Res..