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A note on the multiple partners assignment game


  • Fagebaume, Alexis
  • Gale, David
  • Sotomayor, Marilda


In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International Journal of Game Theory 1, 11-130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322-336] extends this analysis to the case where both types of agents may form more than one partnership and an agent's payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides.

Suggested Citation

  • Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.
  • Handle: RePEc:eee:mateco:v:46:y:2010:i:4:p:388-392

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    References listed on IDEAS

    1. Marilda Sotomayor, 2008. "The Pareto-Stability Concept is a Natural Solution Concept for Discrete Matching Markets with Iindifferences," Working Papers 2008-12, Brown University, Department of Economics.
    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. 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. Daniel Jaume & Jordi Massó & Alejandro Neme, 2012. "The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 161-187, October.
    2. repec:spa:wpaper:2013wpecon02 is not listed on IDEAS
    3. repec:spr:compst:v:76:y:2012:i:2:p:161-187 is not listed on IDEAS
    4. Marilda Sotomayor, 2010. "Stability property of matchings is a natural solution concept in coalitional market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 237-248, March.
    5. Marilda Sotomayor, 2013. "Labor Time Shared In The Assignment Game Generating New Cooperative And Competitive Structures," Working Papers, Department of Economics 2013_02, University of São Paulo (FEA-USP).


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