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Sets in Excess Demand in Ascending Auctions with Unit-Demand Bidders

Author

Listed:
  • Andersson, Tommy

    () (Department of Economics, Lund University)

  • Andersson, Christer

    (Department of Economics, Lund University)

  • Talman, Adolphus Johannes Jan

    () (CentER, Department of Econometrics and Operations Research, Tilburg University)

Abstract

This paper analyzes the problem of selecting a set of items whose prices are to be updated in the next iteration in so called simple ascending auctions with unit-demand bidders. A family of sets called "sets in excess demand" is introduced, and the main results demonstrate that a simple ascending auction always terminates at the minimum Walrasian equilibrium prices if and only if the selection belongs to this family. The paper also specifies a number of properties of the family of sets in excess demand and relate previously proposed selections to it.

Suggested Citation

  • Andersson, Tommy & Andersson, Christer & Talman, Adolphus Johannes Jan, 2010. "Sets in Excess Demand in Ascending Auctions with Unit-Demand Bidders," Working Papers 2010:15, Lund University, Department of Economics, revised 28 Jun 2012.
  • Handle: RePEc:hhs:lunewp:2010_015
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    File URL: http://project.nek.lu.se/publications/workpap/papers/WP10_15.pdf
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    References listed on IDEAS

    as
    1. Tommy Andersson & Christer Andersson, 2012. "Properties of the DGS-Auction Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 113-133, February.
    2. Mishra, Debasis & Talman, Dolf, 2010. "Characterization of the Walrasian equilibria of the assignment model," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 6-20, January.
    3. Atila Abdulkadiroğlu & Tayfun Sönmez & M. Utku Ünver, 2004. "Room assignment-rent division: A market approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 22(3), pages 515-538, June.
    4. de Vries, Sven & Schummer, James & Vohra, Rakesh V., 2007. "On ascending Vickrey auctions for heterogeneous objects," Journal of Economic Theory, Elsevier, vol. 132(1), pages 95-118, January.
    5. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    6. Mishra, Debasis & Parkes, David C., 2009. "Multi-item Vickrey-Dutch auctions," Games and Economic Behavior, Elsevier, vol. 66(1), pages 326-347, May.
    7. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    8. Andersson, Tommy & Svensson, Lars-Gunnar, 2008. "Non-manipulable assignment of individuals to positions revisited," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 350-354, November.
    9. 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.
    10. Alkan, Ahmet & Demange, Gabrielle & Gale, David, 1991. "Fair Allocation of Indivisible Goods and Criteria of Justice," Econometrica, Econometric Society, vol. 59(4), pages 1023-1039, July.
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    Citations

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    Cited by:

    1. Andersson, Tommy & Yang, Zaifu & Zhang, Dongmo, 2015. "How to efficiently allocate houses under price controls?," Economics Letters, Elsevier, vol. 130(C), pages 97-99.
    2. Ingebretsen Carlson, Jim, 2015. "An Approximate Auction," Working Papers 2015:19, Lund University, Department of Economics.
    3. repec:jmi:articl:jmi-v2i1a4 is not listed on IDEAS
    4. Kazuo Murota & Akiyoshi Shioura & Zaifu Yang, 2014. "Time Bounds for Iterative Auctions: A Unified Approach by Discrete Convex Analysis," Discussion Papers 14/27, Department of Economics, University of York.
    5. Serizawa, Shigehiro & Morimoto, Shuhei, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    6. Tommy Andersson & Christer Andersson, 2012. "Properties of the DGS-Auction Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 113-133, February.
    7. Andersson, Tommy & Gudmundsson, Jens & Talman, Dolf & Yang, Zaifu, 2014. "A competitive partnership formation process," Games and Economic Behavior, Elsevier, vol. 86(C), pages 165-177.
    8. Andersson, T. & Erlanson, A. & Gudmundsson, J. & Habis, H. & Ingebretsen Carlson, J. & Kratz, J., 2014. "A method for finding the maximal set in excess demand," Economics Letters, Elsevier, vol. 125(1), pages 18-20.
    9. Andersson, Tommy & Erlanson, Albin, 2013. "Multi-item Vickrey–English–Dutch auctions," Games and Economic Behavior, Elsevier, vol. 81(C), pages 116-129.

    More about this item

    Keywords

    Multi-item auctions; unit-demand; excess demand; algorithms;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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