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On Cooperative Solutions of a Generalized Assignment Game: Limit Theorems to the Set of Competitive Equilibria

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  • Jordi Massó

    ()

  • Alejandro Neme

    ()

Abstract

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

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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 810.10.

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Length: 35
Date of creation: 05 Mar 2010
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Handle: RePEc:aub:autbar:810.10

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Keywords: Assignment game; Core; Set-wise stability; Competitive equilibrium.;

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  1. Edgeworth, Francis Ysidro, 1881. "Mathematical Psychics," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number edgeworth1881.
  2. 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.
  3. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
  4. Paul Milgrom, 2008. "Assignment Messages and Exchanges," Discussion Papers 08-014, Stanford Institute for Economic Policy Research.
  5. Daniel Jaume & Jordi Massó & Alejandro Neme, 2009. "The Multiple-partners Assignment Game with Heterogeneous Sells and Multi-unit Demands: Competitive Equilibria," UFAE and IAE Working Papers 802.09, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  6. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer, vol. 28(4), pages 567-583.
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