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Title

The Multiple-partners Assignment Game with Heterogeneous Sales and Multi-unit Demands: Competitive Equilibria

AuthorsJaume, Daniel; Massó, Jordi; Neme, Alejandro
KeywordsMatching
Assignment Game
Indivisible Goods
Competitive Equilibrium
Lattice
Issue Date5-Mar-2010
CitationUFAE and IAE Working Papers ; 808.10
AbstractA multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.
DescriptionJEL Classification Codes: C78; D78
Publisher version (URL)http://pareto.uab.es/wp/2010/80810.pdf
URIhttp://hdl.handle.net/10261/35046
Appears in Collections:(IAE) Informes y documentos de trabajo
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