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The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes

Author

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  • John Q. Cheng

    (University of Michigan)

  • Michael P. Wellman

    (University of Michigan)

Abstract

The WALRAS algorithm calculates competitive equilibria via a distributed tatonnement-like process, in which agents submit single-good demand functions to market-clearing auctions. The algorithm is asynchronous and decentralized with respect to both agents and markets, making it suitable for distributed implementation. We present a formal description of this algorithm, and prove that it converges under the standard assumption of gross substitutability. We relate our results to the literature on general equilibrium stability and some more recent work on decentralized algorithms. We present some experimental results as well, particularly for cases where the assumptions required to guarantee convergence do not hold. Finally, we consider some extensions and generalizations to the WALRAS algorithm.

Suggested Citation

  • John Q. Cheng & Michael P. Wellman, 1995. "The WALRAS Algorithm: A Convergent Distributed Implementation of General Equilibrium Outcomes," Computational Economics 9508001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpco:9508001
    Note: Type of Document - postscript; pages: 23 ; figures: included. Submitted for publication
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    References listed on IDEAS

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    1. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, September.
    2. Shoven,John B. & Whalley,John, 1992. "Applying General Equilibrium," Cambridge Books, Cambridge University Press, number 9780521266550, September.
    3. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-999, September.
    4. Shafer, Wayne & Sonnenschein, Hugo, 1993. "Market demand and excess demand functions," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 14, pages 671-693, Elsevier.
    5. Hildenbrand, Werner, 1983. "On the "Law of Demand."," Econometrica, Econometric Society, vol. 51(4), pages 997-1019, July.
    6. Campbell,Donald E., 1987. "Resource Allocation Mechanisms," Cambridge Books, Cambridge University Press, number 9780521319904, September.
    7. Reiter, Stanley & Simon, Carl P., 1992. "Decentralized dynamic processes for finding equilibrium," Journal of Economic Theory, Elsevier, vol. 56(2), pages 400-425, April.
    8. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
    9. Alan P. Kirman, 1992. "Whom or What Does the Representative Individual Represent?," Journal of Economic Perspectives, American Economic Association, vol. 6(2), pages 117-136, Spring.
    10. Chipman, John S., 1974. "Homothetic preferences and aggregation," Journal of Economic Theory, Elsevier, vol. 8(1), pages 26-38, May.
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    Cited by:

    1. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
    2. Nielsen, Kurt, 2005. "Auctioning Payment Entitlements," 2005 International Congress, August 23-27, 2005, Copenhagen, Denmark 24566, European Association of Agricultural Economists.
    3. 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.
    4. Bill Gibson, 2007. "A Multi-Agent Systems Approach to Microeconomic Foundations of Macro," UMASS Amherst Economics Working Papers 2007-10, University of Massachusetts Amherst, Department of Economics.
    5. Javad Khazaei & Anthony Downward & Golbon Zakeri, 2014. "Modelling counter-intuitive effects on cost and air pollution from intermittent generation," Annals of Operations Research, Springer, vol. 222(1), pages 389-418, November.
    6. 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.
    7. Wurman, Peter R. & Wellman, Michael P. & Walsh, William E., 2001. "A Parametrization of the Auction Design Space," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 304-338, April.
    8. Eymann, Torsten & Streitberger, Werner & Reinicke, Michael & Freitag, Felix & Chacin, Pablo & Chao, Isaac & Schnizler, Björn & Veit, Daniel, 2007. "Preliminary specification and design documentation for software components to achieve catallaxy in computational systems," Bayreuth Reports on Information Systems Management 2, University of Bayreuth, Chair of Information Systems Management.
    9. Kurt Nielsen & Jesper Troelsgaard Nielsen, 2010. "An Allocatively Efficient Auction Market for Payment Entitlements?," MSAP Working Paper Series 03_2010, University of Copenhagen, Department of Food and Resource Economics.
    10. Dennis J. Zhang & Itai Gurvich & Jan A. Van Mieghem & Eric Park & Robert S. Young & Mark V. Williams, 2016. "Hospital Readmissions Reduction Program: An Economic and Operational Analysis," Management Science, INFORMS, vol. 62(11), pages 3351-3371, November.
    11. Sandholm, Tuomas W. & Lesser, Victor R., 2001. "Leveled Commitment Contracts and Strategic Breach," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 212-270, April.

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    More about this item

    Keywords

    tatonnement; distributed computation; progressive equilibration;
    All these keywords.

    JEL classification:

    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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