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Equilibrium, Auction, Multiple Substitutes and Complements

  • Akiyoshi Shioura
  • Zaifu Yang
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    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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    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
    Contact details of provider: Postal: Department of Economics and Related Studies, University of York, York, YO10 5DD, United Kingdom
    Phone: (0)1904 323776
    Fax: (0)1904 323759
    Web page: http://www.york.ac.uk/economics/
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    1. Robert Day & Paul Milgrom, 2008. "Core-selecting package auctions," International Journal of Game Theory, Springer, vol. 36(3), pages 393-407, March.
    2. 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.
    3. Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
    4. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, 09.
    5. Erdil, Aytek & Klemperer, Paul, 2009. "A New Payment Rule for Core-Selecting Package Auctions," CEPR Discussion Papers 7487, C.E.P.R. Discussion Papers.
    6. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Series Working Papers 2004-W09, University of Oxford, Department of Economics.
    7. Sven de Vries & James Schummer, 2005. "On Ascending Vickrey Auctions for Heterogeneous Objects," 2005 Meeting Papers 389, Society for Economic Dynamics.
    8. 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.
    9. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    10. Paul Klemperer, 2004. "Auctions: Theory and Practice," Economics Papers 2004-W09, Economics Group, Nuffield College, University of Oxford.
    11. Milgrom, Paul, 1998. "Putting auction theory to work : the simultaneous ascending auction," Policy Research Working Paper Series 1986, The World Bank.
    12. 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.
    13. Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. 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).
    15. 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.
    16. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    17. Milgrom, Paul & Strulovici, Bruno, 2009. "Substitute goods, auctions, and equilibrium," Journal of Economic Theory, Elsevier, vol. 144(1), pages 212-247, January.
    18. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
    19. Paul Klemperer, 2004. "Introduction to Auctions: Theory and Practice
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