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On Multi-Object Auctions and Matching Theory: Algorithmic Aspects

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Graph Theory, Combinatorics and Algorithms

Part of the book series: Operations Research/Computer Science Interfaces Series ((volume 34))

Abstract

Auctions are the most widely used strategic game-theoretic mechanisms in the Internet. Auctions have been mostly studied from a game-theoretic and economic perspective, although recent work in AI and OR has been concerned with computational aspects of auctions as well. When faced from a computational perspective, combinatorial auctions are perhaps the most challenging type of auctions. Combinatorial auctions are auctions where buyers may submit bids for bundles of goods. Another interesting direction is that of constrained auctions where some restrictions are imposed upon the set of feasible solutions. Given that finding an optimal allocation of the goods in a combinatorial and/or constrained auction is in general intractable, researchers have been concerned with exposing tractable instances of combinatorial and constrained auctions problems. In this chapter we discuss the use of b-matching techniques in the context of combinatorial and constrained auctions.

Most of the results in this chapter are based on [22, 30, 10].

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References

  1. K. Akcoglu, J. Aspnes, B. DasGupta and M. Kao, Opportunity cost algorithms for combinatorial auctions. Technical Report 2000-27, DIMACS, (2000).

    Google Scholar 

  2. R. P. Anstee, A polynomial algorithm for b-matching: An alternative approach, Information Processing Letters 24: 153–157 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  3. S. A. Cook, The complexity of theorem-proving procedures, Proc. 3rd Ann. ACM Symp. on Theory of Computing, Association for Computing Machinery, New-York, (1971) pp. 151–158.

    Google Scholar 

  4. W. Cook, W. R. Pulleyblank, Linear systems for constrained matching problems, Mathematics of Operations Research 12: 97–120 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  5. T. H. Cormen, C. E. Leiserson, R. L. Rivest, Introduction to algorithms, The MIT Press, Twentieth printing, (1998).

    Google Scholar 

  6. W. H. Cunningham and A. B. March III, A primal algorithm for optimum matching, Mathematical Programming Study 8: 50–72 (1978).

    Google Scholar 

  7. E. Durfee, What your computer really needs to know, you learned in kindergarten. In 10th National Conference on Artificial Intelligence, (1992) pp. 858–864.

    Google Scholar 

  8. Federal communications commission (FCC) at http://www.fcc.gov/auctions.

    Google Scholar 

  9. Y. Fujishima, K. Leyton-Brown, Y. Shoham, Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches, International Joint Conference on Artificial Intelligence (IJCAI), Stockholm, Sweden, (1999).

    Google Scholar 

  10. R. Frank and M. Penn, Optimal allocations in constrained multi-object and combinatorial auctions, in preparation.

    Google Scholar 

  11. A. M. H. Gerards, in Handbooks in Operations Research and Management Science Vol. 7, ed. M.O. Ball, T.L. Magnanti, C.L. Monma, G.L. Nemhauser, “Matching” in Network Models, (1995) pp. 135–212.

    Google Scholar 

  12. M. Grotschel, L. Lovasz, A. Schrijver, Geometric algorithms and combinatorial optimization, Springer-Verlag, Second Corrected Edition, (1993).

    Google Scholar 

  13. S. van Hoesel, R. Müller, Optimization in electronic markets: Examples in combinatorial auctions, Netonomics, 3: 23–33 (2001).

    Google Scholar 

  14. R. Karp, Reducibility among combinatorial problems, in R. Miller and J. Thatcher, editors, Complexity of Computer Computations, Plenum Press, NY, (1972) pp. 85–103.

    Google Scholar 

  15. S. Kraus, Negotiation and cooperation in multi-agent environments, Artificial Intelligence, 94: 79–97 (1997).

    Article  MATH  Google Scholar 

  16. D. Lehmann, L.I. O’Callagham and Y. Shoham, Truth revelation in rapid, approximately efficient combinatorial auctions, In ACM Conference on Electronic Commerce, (1999) pp. 96–102.

    Google Scholar 

  17. L. Lovász and M. D. Plummer, Matching Theory, Akadémiai Kiadó, Budapest (North Holland Mathematics Studies Vol. 121, North Holland, Amsterdam, 1986).

    MATH  Google Scholar 

  18. J. McMillan, Selling spectrum rights, Journal of Economic Perspective 8: 145–162 (1994).

    Google Scholar 

  19. D. Monderer and M. Tennenholtz, Optimal auctions revisited Artificial Intelligence, 120: 29–42 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  20. N. Nisan, Bidding and allocation in combinatorial auctions, in ACM Conference on Electronic Commerce, (2000) pp. 1–12.

    Google Scholar 

  21. D. C. Parkes, ibundel: An Efficient Ascending Price Bundle Auction, in ACM Conference on Electronic Commerce, (1999) pp. 148–157.

    Google Scholar 

  22. M. Penn, M. Tennenholtz, Constrained Multi-Object Auctions, Information Processing Letters 75: 29–34 (2000).

    Article  MathSciNet  Google Scholar 

  23. W. R. Pulleyblank, Facets of matching polyhedra, Ph.D. Thesis, University of Waterloo, Department of Combinatorial Optimization, Canada, (1973).

    Google Scholar 

  24. J. S. Rosenschein and G. Zlotkin, Rules of Encounter, MIT Press, (1994).

    Google Scholar 

  25. A. Roth, FCC Auction (and related matters): Brief Bibliography, in A. Roth’s homepage, Harvard Economics Department and Harvard Business School, USA.

    Google Scholar 

  26. M. H. Rothkopf, A. Pekeč, R. M. Harstad, Computationally Manageable Combinational Auctions, Management Science 44: 1131–1147 (1998).

    Article  MATH  Google Scholar 

  27. T. Sandholm, Limitations of the Vickery auction in computational multiagent systems, Proceedings of the Second International Conference on Multiagent Systems, Keihanna Plaza, Kyoto, Japan, (1996) pp. 299–306.

    Google Scholar 

  28. T. Sandholm, An Algorithm for OptimalWinner Determination in Combinatorial Auctions, International Joint Conference on Artificial Intelligence (IJCAI), pp. 542–547, Stockholm, Sweden, (1999).

    Google Scholar 

  29. M. Tennenholtz, Electronic commerce: From game-theoretic and economic models toworking protocols. In International Joint Conference on Artificial Intelligence (IJCAI), pp. 1420–1425 Stockholm, Sweden, (1999).

    Google Scholar 

  30. M. Tennenholtz, Some Tractable Combinatorial Auctions Artificial Intelligence, 140: 231–243 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  31. S. de Vries, R. V. Vohra, Combinatorial Auctions: A Brief Survey, unpublished manuscript.

    Google Scholar 

  32. M. P. Wellman, W. E. Walsh, P. R. Wurman and J. K. MacKie-Mason, Auction Protocols for Decentralized Scheduling, Games and Economic Behavior, 35: 271–303 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  33. E. Wolfstetter, Auctions: An Introduction, Journal of Economic Surveys, 10: 367–420 (1996).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management Technion, Israel Institute of Technology, Haifa, 32000, Israel

    Michal Penn & Moshe Tennenholtz

Authors
  1. Michal Penn
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  2. Moshe Tennenholtz
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Editor information

Editors and Affiliations

  1. University of Haifa, Israel

    Martin Charles Golumbic  & Irith Ben-Arroyo Hartman  & 

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© 2005 Springer Science + Business Media, Inc.

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Penn, M., Tennenholtz, M. (2005). On Multi-Object Auctions and Matching Theory: Algorithmic Aspects. In: Golumbic, M.C., Hartman, I.BA. (eds) Graph Theory, Combinatorics and Algorithms. Operations Research/Computer Science Interfaces Series, vol 34. Springer, Boston, MA. https://doi.org/10.1007/0-387-25036-0_7

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