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Characterization of the Walrasian equilibria of the assignment model

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  • Mishra, Debasis
  • Talman, Dolf

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 sufficient 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

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 46 (2010)
Issue (Month): 1 (January)
Pages: 6-20

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Handle: RePEc:eee:mateco:v:46:y:2010:i:1:p:6-20

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Web page: http://www.elsevier.com/locate/jmateco

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Keywords: Assignment model Walrasian equilibrium Iterative auctions Overdemanded set Underdemanded set;

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  1. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1483-1504, November.
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  6. Mishra, Debasis & Parkes, David C., 2009. "Multi-item Vickrey-Dutch auctions," Games and Economic Behavior, Elsevier, Elsevier, vol. 66(1), pages 326-347, May.
  7. Sankaran, Jayaram K., 1994. "On a dynamic auction mechanism for a bilateral assignment problem," Mathematical Social Sciences, Elsevier, Elsevier, vol. 28(2), pages 143-150, October.
  8. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer, Springer, vol. 19(4), pages 413-20.
  9. 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.
  10. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, Elsevier, vol. 87(1), pages 95-124, July.
  11. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, Econometric Society, vol. 53(4), pages 873-88, July.
  12. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(4), pages 863-72, August.
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  14. Edward Clarke, 1971. "Multipart pricing of public goods," Public Choice, Springer, Springer, vol. 11(1), pages 17-33, September.
  15. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, Econometric Society, vol. 49(2), pages 437-50, March.
  16. Peter Cramton, 1998. "Ascending Auctions," Papers of Peter Cramton, University of Maryland, Department of Economics - Peter Cramton 98eer, University of Maryland, Department of Economics - Peter Cramton, revised 28 Jul 1998.
  17. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, Elsevier, vol. 92(1), pages 66-95, May.
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Cited by:
  1. ANDERSSON, Tommy & EHLERS, Lars & SVENSSON, Lars-Gunnar, 2010. "Budget-Balance, Fairness and Minimal Manipulability," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2010-09, Universite de Montreal, Departement de sciences economiques.
  2. Tommy Andersson & Lars‐Gunnar Svensson, 2014. "Non‐Manipulable House Allocation With Rent Control," Econometrica, Econometric Society, Econometric Society, vol. 82(2), pages 507-539, 03.
  3. Andersson , Tommy & Yang , Zaifu & Zhang , Dongmo, 2014. "How to Efficiently Allocate Houses under Price Controls?," Working Papers, Lund University, Department of Economics 2014:24, Lund University, Department of Economics.
  4. 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, Econometric Society.
  5. Andersson, Tommy & Erlanson, Albin, 2013. "Multi-item Vickrey–English–Dutch auctions," Games and Economic Behavior, Elsevier, Elsevier, vol. 81(C), pages 116-129.
  6. Andersson , Tommy & Gudmundsson , Jens & Talman , Adolphus & Yang , Zaifu, 2013. "A Competitive Partnership Formation Process," Working Papers, Lund University, Department of Economics 2013:2, Lund University, Department of Economics.

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