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On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game


  • R. Pablo Arribillaga
  • Jordi Massó
  • Alejandro Neme


We study cooperative and competitive solutions for a many- to-many generalization of Shapley and Shubik (1972)'s assignment game. We consider the Core, three other notions of group stability and two alternative definitions of competitive equilibrium. We show that (i) each group stable set is closely related with the Core of certain games defined using a proper notion of blocking and (ii) each group stable set contains the set of payoff vectors associated to the two definitions of competitive equilibrium. We also show that all six solutions maintain a strictly nested structure. Moreover, each solution can be identified with a set of matrices of (discriminated) prices which indicate how gains from trade are distributed among buyers and sellers. In all cases such matrices arise as solutions of a system of linear inequalities. Hence, all six solutions have the same properties from a structural and computational point of view.

Suggested Citation

  • R. Pablo Arribillaga & Jordi Massó & Alejandro Neme, 2013. "On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game," Working Papers 740, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:740

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    References listed on IDEAS

    1. Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
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    Cited by:

    1. 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.

    More about this item


    assignment game; Competitive Equilibrium; core; group stability;

    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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