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Efficiency and Equilibrium in Task Allocation Economics with Hierarchical Dependencies

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  • William E. Walsh
  • Michael P. Wellman

Abstract

We analyze economic efficiency and equilibrium properties in decentralized task allocation problems involving hierarchical dependencies and resource contention. We bound the inefficiency of a type of approximate equilibrium in proportion to the number of agents and the bidding parameters in a particular market protocol. This protocol converges to an approximate equilibrium with respect to all agents, except those which may acquire unneeded inputs. We introduce a decommitment phase to allow such agents to decommit from their input contracts. Experiments indicate that the augmented market protocol produces highly efficient allocations on average.

Suggested Citation

  • William E. Walsh & Michael P. Wellman, 1999. "Efficiency and Equilibrium in Task Allocation Economics with Hierarchical Dependencies," Working Papers 99-07-049, Santa Fe Institute.
  • Handle: RePEc:wop:safiwp:99-07-049
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    References listed on IDEAS

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    1. Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    4. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    5. Peter R. Wurman & Michael P. Wellman, 1999. "Equilibrium Prices in Bundle Auctions," Working Papers 99-09-064, Santa Fe Institute.
    6. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    7. R. Preston McAfee & John McMillan, 1996. "Analyzing the Airwaves Auction," Journal of Economic Perspectives, American Economic Association, vol. 10(1), pages 159-175, Winter.
    8. Gul, F. & Stacchetti, E., 1997. "Walrasian Equilibrium Without Complementarities," Papers 97-03, Michigan - Center for Research on Economic & Social Theory.
    9. Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
    10. McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June.
    11. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
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    Cited by:

    1. 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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    Keywords

    Supply chain formation; competitive equilibrium; distributed systems;

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