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Multi-agent Learning for Winner Determination in Combinatorial Auctions

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Book cover Modern Advances in Applied Intelligence (IEA/AIE 2014)

Abstract

The winner determination problem (WDP) in combinatorial double auctions suffers from computation complexity. In this paper, we attempt to solve the WDP in combinatorial double auctions based on an agent learning approach. Instead of finding the exact solution, we will set up a fictitious market based on multi-agent system architecture and develop a multi-agent learning algorithm to determine the winning bids in the fictitious market to reduce the computational complexity in solving the WDP in combinatorial double auctions. In the fictitious market, each buyer and each seller is represented by an agent. There is a mediator agent that represents the mediator. The issue is to develop learning algorithms for all the agents in the system to collectively solve the winner determination problem for combinatorial double auctions. In this paper, we adopt a Lagrangian relaxation approach to developing efficient multi-agent learning algorithm for solving the WDP in combinatorial double auctions. Numerical results indicate our agent learning approach is more efficient than the centralized approach.

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References

  1. Andersson, A., Tenhunen, M., Ygge, F.: Integer programming for combinatorial auction winner determination. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 39–46 (2000)

    Google Scholar 

  2. Beard, R.W., McLain, T.W., Goodrich, M.A., Anderson, E.P.: Coordinated target assignment and intercept for unmanned air vehicles. IEEE Transactions on Robotics and Automation 18(6), 911–922 (2002)

    Article  Google Scholar 

  3. de Vries, S., Vohra, R.V.: Combinatorial Auctions: A Survey. INFORMS Journal on Computing (3), 284–309 (2003)

    Google Scholar 

  4. Perugini, D., Lambert, D., Sterling, L., Pearce, A.: From Single Static to Multiple Dynamic Combinatorial Auctions. In: IEEE/WIC/ACM International Conference on Intelligent Agent Technology, September 19-22, pp. 443–446 (2005)

    Google Scholar 

  5. Fujishima, Y., Leyton-Brown, K., Shoham, Y.: Taming the computational complexity of combinatorial auctions: Optimal and approximate approaches. In: Sixteenth International Joint Conference on Artificial Intelligence, pp. 548–553 (1999)

    Google Scholar 

  6. Fisher, M.L.: Lagrangian relaxation method for solving integer programming problems. Management Science 27, 1–18 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gonen, R., Lehmann, D.: Optimal solutions for multi-unit combinatorial auctions: branch and bound heuristics. In: The Proceedings of the Second ACM Conference on Electronic Commerce (EC 2000), pp. 13–20 (2000)

    Google Scholar 

  8. Guo, Y., Lim, A., Rodrigues, B., Tang, J.: Using a Lagrangian heuristic for a combinatorial auction problem. In: Proceedings of the 17th IEEE International Conference on Tools with Artificial Intelligence (2005)

    Google Scholar 

  9. Murphey, R.A.: Target-based weapon target assignment problems. In: Pardalos, P.M., Pitsoulis, L.S. (eds.) Nonlinear Assignment Problems: Algorithms and Applications, pp. 39–53. Kluwer Academic Publishers, Dordrecht (1999)

    Google Scholar 

  10. Hoos, H.H., Boutilier, C.: Solving combinatorial auctions using stochastic local search. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 22–29 (2000)

    Google Scholar 

  11. Hsieh, F.-S.: Combinatorial reverse auction based on revelation of Lagrangian multipliers. Decision Support Systems 48(2), 323–330 (2010)

    Article  Google Scholar 

  12. Ahuja, R.K., Kumar, A., Jha, K., Orlin, J.B.: Exact and heuristic methods for the weapon-target assignment problem. Technical Report #4464-03, MIT, Sloan School of Management Working Papers (2003)

    Google Scholar 

  13. Jones, J.L., Koehler, G.J.: Combinatorial auctions using rule-based bids. Decision Support Systems 34, 59–74 (2002)

    Article  Google Scholar 

  14. Pekeč, A., Rothkopf, M.H.: Combinatorial auction design. Management Science 49, 1485–1503 (2003)

    Article  MATH  Google Scholar 

  15. Polyak, B.T.: Minimization of Unsmooth Functionals. USSR Computational Math. and Math. Physics 9, 14–29 (1969)

    Article  Google Scholar 

  16. Rothkopf, M., Pekeč, A., Harstad, R.: Computationally manageable combinational auctions. Management Science 44, 1131–1147 (1998)

    Article  MATH  Google Scholar 

  17. Sandholm, T.: An algorithm for optimal winner determination in combinatorial auctions. In: Proc. IJCAI 1999, Stockholm, pp. 542–547 (1999)

    Google Scholar 

  18. Sandholm, T.: Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence 135(1-2), 1–54 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  19. Sandholm, T.: Approaches to winner determination in combinatorial auctions. Decision Support Systems 28, 165–176 (2000)

    Article  Google Scholar 

  20. Vemuganti, R.R.: Applications of set covering, set packing and set partitioning models: a survey. In: Du, D.-Z. (ed.) Handbook of Combinatorial Optimization, vol. 1, pp. 573–746. Kluwer Academic Publishers, Netherlands (1998)

    Chapter  Google Scholar 

  21. Yanga, S., Segrea, A.M., Codenottib, B.: An optimal multiprocessor combinatorial auction solver. Computers & Operations Research 36, 149–166 (2007)

    Article  Google Scholar 

  22. Xia, M., Stallaert, J., Whinston, A.B.: Solving the combinatorial double auction problem. European Journal of Operational Research 164, 239–251 (2005)

    Article  MATH  Google Scholar 

  23. Hsieh, F.-S., Lin, J.-B.: Assessing the benefits of group-buying based combinatorial reverse auctions. Electronic Commerce Research and Applications 11(4), 407–419 (2012)

    Article  Google Scholar 

  24. Hsieh, F.-S., Lin, J.-B.: Virtual enterprises partner selection based on reverse auction. International Journal of Advanced Manufacturing Technology 62, 847–859 (2012)

    Article  Google Scholar 

  25. Gordon, G.J., Varakantham, P.R., Yeoh, W., Lau, H.C., Aravamudhan, A.S., Cheng, S.-F.: Lagrangian relaxation for large-scale multi-agent planning. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012), vol. 3, pp. 1227–1228 (2012)

    Google Scholar 

  26. Geoffrey, J.: Gordon, Agendas for multi-agent learning. Artificial Intelligence 171(7), 392–401 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  27. Akella, R., Kumar, P.R.: Optimal control of production rate in a failure-prone manufacturing systems. IEEE Transactions on Automatic Control 31(2), 116–126 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  28. Gershwin, S.B.: Manufacturing Systems Engineering. Prentice-Hall, Englewood Cliffs (1994)

    Google Scholar 

  29. Kimemia, J., Gershwin, S.B.: An algorithm for the computer control of a fexible manufacturing system. IIE Transactions 15(4), 353–362 (1983)

    Article  Google Scholar 

  30. Kumar, P.R.: Re-entrant lines. Queueing Systems: Theory and Applications 13, 87–110 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  31. Altman, E., Boulogne, T., El Azouzi, R., Jiménez, T., Wynter, L.: A survey on networking games in telecommunications. Computers and Operations Research 33(2), 286–311 (2005)

    Article  Google Scholar 

  32. Altman, E., Shimkin, N.: Individual equilibrium and learning in processor sharing systems. Operations Research 46, 776–784 (1998)

    Article  MATH  Google Scholar 

  33. La, R., Anantharam, V.: Optimal routing control: Repeated game approach. IEEE Transactions on Automatic Control 47(3), 437–450 (2002)

    Article  MathSciNet  Google Scholar 

  34. Orda, A., Rom, R., Shimkin, N.: Competitive routing in multi-user communication networks. IEEE/ACM Trans. Networking 1(5), 510–521 (1993)

    Article  Google Scholar 

  35. Roughgarden, T.: Selish Routing and the Price of Anarchy. MIT Press, Cambridge (2005)

    Google Scholar 

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Hsieh, FS., Liao, CS. (2014). Multi-agent Learning for Winner Determination in Combinatorial Auctions. In: Ali, M., Pan, JS., Chen, SM., Horng, MF. (eds) Modern Advances in Applied Intelligence. IEA/AIE 2014. Lecture Notes in Computer Science(), vol 8481. Springer, Cham. https://doi.org/10.1007/978-3-319-07455-9_1

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  • DOI: https://doi.org/10.1007/978-3-319-07455-9_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07454-2

  • Online ISBN: 978-3-319-07455-9

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