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Equilibrium, Auction, Multiple Substitutes and Complements

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  • Akiyoshi Shioura
  • Zaifu Yang
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    Abstract

    We study a market model where there are n different types of indivisible goods for sale. The goods can be substitutable or complementary. There are multiple units of each good. Each agent may consume several goods and has quasi-linear utilities in money. We introduce a general condition which will be shown to guarantee the existence of a Walrasian equilibrium and generalize several existing conditions such as gross substitutes, strong substitutes, and gross substitutes and complements. We also identify several characterizations of this condition. Furthermore, we propose a price adjustment process which converges globally to a Walrasian equilibrium.

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    File URL: http://www.york.ac.uk/media/economics/documents/discussionpapers/2013/1317.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of York in its series Discussion Papers with number 13/17.

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    Date of creation: Jul 2013
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    Handle: RePEc:yor:yorken:13/17

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    Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
    Phone: (0)1904 323776
    Fax: (0)1904 323759
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    Web page: http://www.york.ac.uk/economics/
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    Related research

    Keywords: Indivisibility; equilibrium; existence; substitutes and complements; auction;

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    References

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    1. Lawrence M. Ausubel & Paul Milgrom, 2002. "Ascending Auctions with Package Bidding," Working Papers 02004, Stanford University, Department of Economics.
    2. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, 09.
    3. Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
    4. Erdil, Aytek & Klemperer, Paul, 2009. "A New Payment Rule for Core-Selecting Package Auctions," CEPR Discussion Papers 7487, C.E.P.R. Discussion Papers.
    5. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    6. MISHRA, Debasis & PARKES, David C., 2005. "Ascending price Vickrey auctions for general valuations," CORE Discussion Papers 2005052, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
    8. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    9. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford.
    10. Jinpeng Ma, 1998. "Competitive Equilibrium with Indivisibilities," Departmental Working Papers 199809, Rutgers University, Department of Economics.
    11. Sven de Vries & James Schummer, 2005. "On Ascending Vickrey Auctions for Heterogeneous Objects," 2005 Meeting Papers 389, Society for Economic Dynamics.
    12. 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.
    13. Paul Klemperer, 2004. "Introduction to Auctions: Theory and Practice
      [Auctions: Theory and Practice]
      ," Introductory Chapters, Princeton University Press.
    14. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    15. 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.
    16. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    17. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    18. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, 05.
    19. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
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