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Characterization of the walrasian equilibria of the assignment model

  • Debasis Mishra


    (Indian Statistical Institute, New Delhi)

  • Dolf Talman

    (Tilburg University Institute, New Delhi)

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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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. 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.
  2. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
  3. 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.
  4. 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.
  5. 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.
  6. Cramton, Peter, 1998. "Ascending auctions," European Economic Review, Elsevier, vol. 42(3-5), pages 745-756, May.
  7. Sotomayor, Marilda, 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), July.
  8. 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.
  9. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
  10. Sven de Vries & James Schummer, 2005. "On Ascending Vickrey Auctions for Heterogeneous Objects," 2005 Meeting Papers 389, Society for Economic Dynamics.
  11. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
  12. 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.
  13. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, 03.
  14. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, vol. 11(1), pages 17-33, September.
  15. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
  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. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July.
  18. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer, vol. 19(4), pages 413-20.
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