Ascending Combinatorial Auctions with Allocation Constraints: On Game Theoretical and Computational Properties of Generic Pricing Rules

Combinatorial auctions are used in a variety of application domains, such as transportation or industrial procurement, using a variety of bidding languages and different allocation constraints. This flexibility in the bidding languages and the allocation constraints is essential in these domains but has not been considered in the theoretical literature so far. In this paper, we analyze different pricing rules for ascending combinatorial auctions that allow for such flexibility: winning levels and deadness levels. We determine the computational complexity of these pricing rules and show that deadness levels actually satisfy an ex post equilibrium, whereas winning levels do not allow for a strong game theoretical solution concept. We investigate the relationship of deadness levels and the simple price update rules used in efficient ascending combinatorial auction formats. We show that ascending combinatorial auctions with deadness level pricing rules maintain a strong game theoretical solution concept and r...

[1]  Subhash Suri,et al.  Side constraints and non-price attributes in markets , 2006, Games Econ. Behav..

[2]  Karl-Martin Ehrhart,et al.  Design of the 3G Spectrum Auctions in the UK and Germany: An Experimental Investigation , 2005 .

[3]  Thomas Sandholm,et al.  Making Markets and Democracy Work: A Story of Incentives and Computing , 2003, IJCAI.

[4]  Yoav Shoham,et al.  Towards a universal test suite for combinatorial auction algorithms , 2000, EC '00.

[5]  P. Pardalos,et al.  Minimax and applications , 1995 .

[6]  Shawn P. Curley,et al.  Effect of Information Feedback on Bidder Behavior in Continuous Combinatorial Auctions , 2012, Manag. Sci..

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

[8]  K. Ko,et al.  On the Complexity of Min-Max Optimization Problems and their Approximation , 1995 .

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

[10]  Martin Bichler,et al.  Efficiency with linear prices: a theoretical and experimental analysis of the combinatorial clock auction. , 2010, EC '10.

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

[12]  Andrew B. Whinston,et al.  A Market-Based Optimization Algorithm for Distributed Systems , 2007, Manag. Sci..

[13]  Martin Bichler,et al.  Designing smart markets , 2010 .

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

[15]  Subhash Suri,et al.  Market Clearability , 2001, IJCAI.

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

[17]  Vincent Conitzer,et al.  Vote elicitation: complexity and strategy-proofness , 2002, AAAI/IAAI.

[18]  Craig Boutilier,et al.  Bidding Languages for Combinatorial Auctions , 2001, IJCAI.

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

[20]  Martin Bichler,et al.  Research Commentary - Designing Smart Markets , 2010, Inf. Syst. Res..

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

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

[23]  Jan Stallaert,et al.  A Market Design for Grid Computing , 2008, INFORMS J. Comput..

[24]  Shawn P. Curley,et al.  A Data-Driven Exploration of Bidder Strategies in Continuous Combinatorial Auctions , 2008 .

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

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

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

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

[29]  P. Keskinocak,et al.  Bidding strategies and their impact on revenues in combinatorial auctions , 2005 .

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

[31]  Christos H. Papadimitriou,et al.  Approximability and completeness in the polynomial hierarchy , 2000 .

[32]  Salil P. Vadhan,et al.  Computational Complexity , 2005, Encyclopedia of Cryptography and Security.

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

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

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

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

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

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

[39]  C. Caplice.  Electronic Markets for Truckload Transportation , 2007 .

[40]  K. Engel.  Sperner Theory , 1996 .

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

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

[43]  Konrad Engel,et al.  Sperner Theory: Index , 1996 .

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

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

[46]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .

[47]  Andrew B. Whinston,et al.  Pricing combinatorial auctions , 2004, Eur. J. Oper. Res..

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

[49]  Noam Nisan,et al.  Multi-unit Auctions with Budget Limits , 2008, 2008 49th Annual IEEE Symposium on Foundations of Computer Science.

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