Web based computerised auctions are increasingly present in the Internet, and we can imagine that in the future automated buyer and seller agents will conduct automated transactions in this manner. The purpose of this paper is to model automated bidders and sellers which interact through a computerised auction. We model bidding process using random processes with discrete state-space. We obtain analytical solutions for a variety of single auction models, including English and Vickrey auctions, and relate the income per unit time to the other parameters including the rate of arrival of bids, the seller’s decision time, the value of the good, and the “rest time” of the seller between successive auctions. We examine how the seller’s “decision time” impacts the expected income per unit time received by the seller, and illustrate its effect via numerical examples.


Decision Time Rest Time English Auction Seller Agent Vickrey Auction 
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  1. 1.
    Chow, Y.S., Moriguti, S., Robbins, H., Samuels, S.M.: Optimal selection based on relative rank (the Secretary problem). Israel J. Math. 2, 81–90 (1964)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Gelenbe, E., Mitrani, I.: Analysis and Synthesis of Computer Systems. Academic Press, New York, London (1980)MATHGoogle Scholar
  3. 3.
    Milgrom, P.R., Weber, R.: A theory of auctions and competitive bidding. Econometrica 50, 1089–1122 (1982)MATHCrossRefGoogle Scholar
  4. 4.
    McAfee, R.P., McMillan, J.: Auctions and bidding. J. Economic Literature 25, 699–738 (1987)Google Scholar
  5. 5.
    Gelenbe, E.: Learning in the recurrent random neural network. Neural Computation 5(1), 154–164 (1993)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Medhi, J.: Stochastic Processes, 2nd edn. Wiley Eastern Ltd., New Delhi (1994)MATHGoogle Scholar
  7. 7.
    Gelenbe, E., Pujolle, G.: Introduction to Networks of Queues, 2nd edn. J. Wiley & Sons, Chichester (1998)Google Scholar
  8. 8.
    Shehory, O.: Optimality and risk in purchase from multiple auctions. In: Klusch, M., Zambonelli, F. (eds.) CIA 2001. LNCS (LNAI), vol. 2182, pp. 142–153. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Shehory, O.: Optimal bidding in multiple concurrent auctions. International Journal of Cooperative Information Systems 11(3-4), 315–327 (2002)CrossRefGoogle Scholar
  10. 10.
    Finch, S.R.: Optimal stopping constants, Mathematical Constants, pp. 361–363. Cambridge Univ. Press, Cambridge (2003)Google Scholar
  11. 11.
    Dash, N.R., Jennings, N.R., Parkes, D.C.: Computational mechanism design: a call to arms. IEEE Intelligent Systems, 40–47 (November-December 2003)Google Scholar
  12. 12.
    David, E., Rogers, A., Schiff, J., Kraus, S., Jennings, N.R.: Optimal design of English auctions with discrete bid levels. In: Proc. of 6th ACM Conference on Electronic Commerce (EC 2005), Vancouver, Canada, pp. 98–107 (2005)Google Scholar
  13. 13.
    Fatima, S., Wooldridge, M., Jennings, N.R.: Sequential auctions for objects with common and private values. In: Proc. 4th Int Joint Conf on Autonomous Agents and Multi-Agent Systems, Utrecht, Netherlands, pp. 635–642 (2005)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Erol Gelenbe
    • 1
  1. 1.Intelligent Systems and Networks Group, Electrical and Electronic Engineering DepartmentImperial CollegeLondonUK

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