IDEAS home Printed from https://ideas.repec.org/p/aub/autbar/940.13.html
   My bibliography  Save this paper

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

Author

Listed:
  • R. Pablo Arribillaga

    ()

  • Jordi Massó

    ()

  • Alejandro Neme

    ()

Abstract

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 al- ternative 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 ma- trices 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," UFAE and IAE Working Papers 940.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  • Handle: RePEc:aub:autbar:940.13
    as

    Download full text from publisher

    File URL: http://pareto.uab.es/wp/2013/94013.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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

    Keywords

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:aub:autbar:940.13. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Xavier Vila). General contact details of provider: http://edirc.repec.org/data/ufuabes.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.