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Characterization of the walrasian equilibria of the assignment model

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Author Info
Debasis Mishra () (Indian Statistical Institute, New Delhi)
Dolf Talman (Tilburg University Institute, New Delhi)

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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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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
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Handle: RePEc:ind:isipdp:08-07

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Find related papers by JEL classification:
D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
C69 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Other
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions

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  1. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July. [Downloadable!] (restricted)
  2. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July. [Downloadable!] (restricted)
  6. Groves, Theodore, 1973. "Incentives in Teams," Econometrica, Econometric Society, vol. 41(4), pages 617-31, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, 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, Graduate School of Economics, Getulio Vargas Foundation (Brazil), vol. 56(3), April. [Downloadable!]
  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March. [Downloadable!] (restricted)
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