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

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Abstract

A multiple-partners assignment game with heterogeneous sells and multi-unit 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 only using linear programming. We show 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 equilibrium assignments, and vice versa. We also show that the set of (restricted) equilibrium price vectors has a natural lattice structure and we study how this structure is translated into the set of agents' utilities that are attainable at equilibrium.

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Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 802.09.

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Length: 39
Date of creation: 26 Jul 2009
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Handle: RePEc:aub:autbar:802.09

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Keywords: Matching; Assignment Game; Indivisible Goods; Competitive Equilibrium; Lattice;

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  1. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May.
  2. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer, Springer, vol. 28(4), pages 567-583.
  3. Sotomayor, Marilda, 2003. "Some further remark on the core structure of the assignment game," Mathematical Social Sciences, Elsevier, Elsevier, vol. 46(3), pages 261-265, December.
  4. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, Elsevier, vol. 52(2), pages 152-161, September.
  5. Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.
  6. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 91(3), pages 461-79, June.
  7. Bikhchandani, Sushil & Ostroy, Joseph M., 2002. "The Package Assignment Model," Journal of Economic Theory, Elsevier, vol. 107(2), pages 377-406, December.
  8. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780195102680, October.
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Cited by:
  1. Jordi Massó & Alejandro Neme, 2010. "On Cooperative Solutions of a Generalized Assignment Game: Limit Theorems to the Set of Competitive Equilibria," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 810.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Francisco Robles & Marina Núñez, 2014. "One-seller assignment markets with multiunit demands," UB Economics Working Papers 2014/316, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.

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