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Characterization of the walrasian equilibria of the assignment model

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  • Debasis Mishra

    ()
    (Indian Statistical Institute, New Delhi)

  • Dolf Talman

    (Tilburg University Institute, New Delhi)

Abstract

We study the assignment model where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the extreme and interior points of the set of Walrasian equilibrium price vectors for this model. Our characterizations are in terms of demand sets of buyers. Using these characterizations, we also give a unique characterization of the minimum and the maximum Walrasian equilibrium price vectors. Also, necessary and suncient conditions are given under which the interior of the set of Walrasian equilibrium price vectors is non-empty. Several of the results are derived by interpreting Walrasian equilibrium price vectors as potential functions of an appropriate directed graph.

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Bibliographic Info

Paper provided by Indian Statistical Institute, New Delhi, India in its series Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers with number 08-07.

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Length: 29 pages
Date of creation: Oct 2008
Date of revision:
Handle: RePEc:ind:isipdp:08-07

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  1. Marilda Sotomayor, 2002. "A Simultaneous Descending Bid Auction for Multiple Items and Unitary Demand," Revista Brasileira de Economia, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 56(3), pages 497-510, July.
  2. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  3. Peter Cramton, 1998. "Ascending Auctions," Papers of Peter Cramton 98eer, University of Maryland, Department of Economics - Peter Cramton, revised 28 Jul 1998.
  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 & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-72, August.
  6. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
  7. Sankaran, Jayaram K., 1994. "On a dynamic auction mechanism for a bilateral assignment problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 143-150, October.
  8. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  9. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  10. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
  11. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  12. Debasis Mishra & David C. Parkes, 2007. "Multi-item Vickrey-Dutch auctions," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 07-04, Indian Statistical Institute, New Delhi, India.
  13. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  14. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-79, June.
  15. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer, vol. 19(4), pages 413-20.
  16. Roth, Alvin E. & Sotomayor, Marilda, 1988. "Interior points in the core of two-sided matching markets," Journal of Economic Theory, Elsevier, vol. 45(1), pages 85-101, June.
  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.
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Cited by:
  1. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Cahiers de recherche 18-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. 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.
  3. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, vol. 82(2), pages 507-539, 03.
  4. Andersson, Tommy & Erlanson, Albin, 2012. "Multi-Item Vickery-English-Dutch Auctions," Working Papers 2012:17, Lund University, Department of Economics, revised 15 Jan 2013.
  5. Serizawa, Shigehiro & Morimoto, Shuhei, 0. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society.
  6. Andersson , Tommy & Yang , Zaifu & Zhang , Dongmo, 2014. "How to Efficiently Allocate Houses under Price Controls?," Working Papers 2014:24, Lund University, Department of Economics.

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