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

Daniel Jaume (), Jordi Masso and Alejandro Neme ()

UFAE and IAE Working Papers from Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC)

Abstract: A 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.

Keywords: Matching; Assignment Game; Indivisible Goods; Competitive Equilibrium; Lattice. (search for similar items in EconPapers)
JEL-codes: C78 D78 (search for similar items in EconPapers)
Pages: 40
Date: 2010-03-05
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria (2012)
Working Paper: The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria (2009)
Working Paper: The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria
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Persistent link: https://EconPapers.repec.org/RePEc:aub:autbar:808.10

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