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On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria

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  • Massó, Jordi
  • Neme, Alejandro

Abstract

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We establish that the Set-wise stable set is contained in the Core and contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Second, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. 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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  • Massó, Jordi & Neme, Alejandro, 2014. "On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria," Journal of Economic Theory, Elsevier, vol. 154(C), pages 187-215.
    • Handle: RePEc:eee:jetheo:v:154:y:2014:i:c:p:187-215
    DOI: 10.1016/j.jet.2014.09.016
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    1. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 152-161, September.
    2. Myrna Wooders, 2010. "Cores of many-player games; nonemptiness and equal treatment," Review of Economic Design, Springer;Society for Economic Design, vol. 14(1), pages 131-162, March.
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    Cited by:

    1. Cao, Zhigang & Qin, Chengzhong & Yang, Xiaoguang, 2018. "Shapley's conjecture on the cores of abstract market games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 466-477.

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    More about this item

    Keywords

    Assignment game; Core; Set-wise stability; Competitive equilibrium;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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