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

Author

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  • R. Pablo Arribillaga
  • Jordi Massó
  • Alejandro Neme

Abstract

We study cooperative and competitive solutions for a many-to-many generalization of Shapley and Shubik’s (1971) 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 to 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 with 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, 2014. "On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-20, April.
    • Handle: RePEc:hin:jnljam:190614
    DOI: 10.1155/2014/190614
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    References listed on IDEAS

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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. Paul Milgrom, 2009. "Assignment Messages and Exchanges," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 95-113, August.
    3. Marilda Sotomayor, 1992. "The Multiple Partners Game," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 17, pages 322-354, Palgrave Macmillan.
    4. 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 School of Economics Working Papers 2014/316, University of Barcelona School of Economics.

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    More about this item

    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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