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Nash Equilibrium and Decentralized Negotiation in Auctioning Divisible Resources

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  • Rajiv T. Maheswaran

    (University of Illinois at Urbana-Champaign)

  • Tamer Başar

    (University of Illinois at Urbana-Champaign)

Abstract

We consider the problem of software agents being used as proxies for the procurement of computational and network resources. Mechanisms such as single-good auctions and combinatorial auctions are not applicable for the management of these services, as assigning an entire resource to a single agent is often undesirable and appropriate bund sizes are difficult to determine. We investigate a divisible auction that is proportionally fair. By introducing the notion of price and demand functions that characterize optimal response functions of the bidders, we are able to prove that this mechanism has a unique Nash equilibrium for an arbitrary number of agents with heterogeneous quasilinear utilities. We also describe decentralized negotiation strategies which, with approrpate relaxation, converge locally to the equilibrium point. Given an agent with a sequence of jobs, we show how our analysis holds for a wide variety of objectives.

Suggested Citation

  • Rajiv T. Maheswaran & Tamer Başar, 2003. "Nash Equilibrium and Decentralized Negotiation in Auctioning Divisible Resources," Group Decision and Negotiation, Springer, vol. 12(5), pages 361-395, September.
    • Handle: RePEc:spr:grdene:v:12:y:2003:i:5:d:10.1023_b:grup.0000003745.98183.8d
    DOI: 10.1023/B:GRUP.0000003745.98183.8d
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    References listed on IDEAS

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    1. Cheng, John Q & Wellman, Michael P, 1998. "The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes," Computational Economics, Springer;Society for Computational Economics, vol. 12(1), pages 1-24, August.
    2. Mackie-Mason, J.K. & Varian, H.R., 1993. "Pricing the Internet," Memorandum 1993_020, Oslo University, Department of Economics.
    3. Leon A Petrosyan & Nikolay A Zenkevich, 2016. "Game Theory," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9824, March.
    4. Wellman, Michael P. & Walsh, William E. & Wurman, Peter R. & MacKie-Mason, Jeffrey K., 2001. "Auction Protocols for Decentralized Scheduling," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 271-303, April.
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    Cited by:

    1. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    2. Daron Acemoglu & Asuman Ozdaglar, 2007. "Competition and Efficiency in Congested Markets," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 1-31, February.
    3. Ioannis Caragiannis & Alexandros A. Voudouris, 2021. "The Efficiency of Resource Allocation Mechanisms for Budget-Constrained Users," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 503-523, May.
    4. N. A. Korgin & V. O. Korepanov, 2017. "Experimental Gaming Comparison of Resource Allocation Rules in Case of Transferable Utilities," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-11, June.
    5. Amin Nezarat & GH Dastghaibifard, 2015. "Efficient Nash Equilibrium Resource Allocation Based on Game Theory Mechanism in Cloud Computing by Using Auction," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-29, October.

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