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Walrasian's characterization and a universal ascending auction

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  • Ben-Zwi, Oren

Abstract

We introduce a novel characterization of all Walrasian price vectors in terms of over- and under demanded sets for monotone gross substitute combinatorial auctions.

Suggested Citation

  • Ben-Zwi, Oren, 2017. "Walrasian's characterization and a universal ascending auction," Games and Economic Behavior, Elsevier, vol. 104(C), pages 456-467.
    • Handle: RePEc:eee:gamebe:v:104:y:2017:i:c:p:456-467
    DOI: 10.1016/j.geb.2017.05.013
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    1. T. Andersson & C. Andersson & A. Talman, 2013. "Sets in excess demand in simple ascending auctions with unit-demand bidders," Annals of Operations Research, Springer, vol. 211(1), pages 27-36, December.
    2. Jos A.M. Potters & Anita van Gellekom & Hans Reijnierse, 2002. "Verifying gross substitutability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(4), pages 767-776.
    3. 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.
    4. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions I: Demand Queries," Discussion Paper Series dp381, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    5. Blumrosen, Liad & Nisan, Noam, 2010. "Informational limitations of ascending combinatorial auctions," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1203-1223, May.
    6. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    7. Peter Cramton & John McMillan & Paul Milgrom & Bradley Miller & Bridger Mitchell & Daniel Vincent & Robert Wilson, 1998. "Simultaneous Ascending Auctions with Package Bidding," Papers of Peter Cramton 98cra2, University of Maryland, Department of Economics - Peter Cramton.
    8. 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.
    9. Mishra, D. & Talman, A.J.J., 2010. "Characterization of the Walrasian equilibria of the assignment model," Other publications TiSEM 3e249b02-c0f4-4ccf-bd37-f, Tilburg University, School of Economics and Management.
    10. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    11. Cramton, Peter, 1998. "Ascending auctions," European Economic Review, Elsevier, vol. 42(3-5), pages 745-756, May.
    12. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    13. Liad Blumrosen & Noam Nisan, 2005. "On the Computational Power of Iterative Auctions II: Ascending Auctions," Discussion Paper Series dp382, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. 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.
    15. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    16. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    17. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    18. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429, April.
    19. Satoru Fujishige & Zaifu Yang, 2003. "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 463-469, August.
    20. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
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    Cited by:

    1. Bavly, Gilad & Heller, Yuval & Schreiber, Amnon, 2022. "Social welfare in search games with asymmetric information," Journal of Economic Theory, Elsevier, vol. 202(C).
    2. Oren Ben-Zwi & Ilan Newman, 2023. "No Ascending Auction can find Equilibrium for SubModular valuations," Papers 2312.00522, arXiv.org.
    3. Eric Balkanski & Renato Paes Leme, 2020. "On the Construction of Substitutes," Mathematics of Operations Research, INFORMS, vol. 45(1), pages 272-291, February.

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    More about this item

    Keywords

    Ascending auctions; Characterization; Gross substitute; Walrasian;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D59 - Microeconomics - - General Equilibrium and Disequilibrium - - - Other
    • D69 - Microeconomics - - Welfare Economics - - - Other

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