Characterization of the Walrasian equilibria of the assignment model

D. Mishra, A.J.J. Talman

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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 sufficient conditions are given under which the interior of the set ofWalrasian 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.
Original languageEnglish
Pages (from-to)6-20
JournalJournal of Mathematical Economics
Volume46
Issue number1
Publication statusPublished - 2010

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Walrasian Equilibrium
Assignment
Indivisible
Directed graphs
Interior Point
Extreme Points
Potential Function
Model
Directed Graph
Interior
Necessary Conditions
Walrasian equilibrium
Assignment model
Equilibrium price
Sufficient Conditions

Cite this

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title = "Characterization of the Walrasian equilibria of the assignment model",
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 ofWalrasian 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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Characterization of the Walrasian equilibria of the assignment model. / Mishra, D.; Talman, A.J.J.

In: Journal of Mathematical Economics, Vol. 46, No. 1, 2010, p. 6-20.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Characterization of the Walrasian equilibria of the assignment model

AU - Mishra, D.

AU - Talman, A.J.J.

N1 - Appeared earlier as CentER DP 2006-84 (rt)

PY - 2010

Y1 - 2010

N2 - 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 ofWalrasian 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.

AB - 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 ofWalrasian 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.

M3 - Article

VL - 46

SP - 6

EP - 20

JO - Journal of Mathematical Economics

JF - Journal of Mathematical Economics

SN - 0304-4068

IS - 1

ER -