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A Generalized Assignment Game

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  • Ester Cami?

Abstract

The proposed game is a natural extension of the Shapley and Shubik Assignment Game to the case where each seller owns a set of different objets instead of only one indivisible object. We propose definitions of pairwise stability and group stability that are adapted to our framework. Existence of both pairwise and group stable outcomes is proved. We study the structure of the group stable set and we finally prove that the set of group stable payoffs forms a complete lattice with one optimal group stable payoff for each side of the market.

Suggested Citation

  • Ester Cami?, 2002. "A Generalized Assignment Game," UFAE and IAE Working Papers 514.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    • Handle: RePEc:aub:autbar:514.02
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    References listed on IDEAS

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    1. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    2. Marilda Sotomayor, 1992. "The Multiple Partners Game," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 17, pages 322-354, Palgrave Macmillan.
    3. Charles Blair, 1988. "The Lattice Structure of the Set of Stable Matchings with Multiple Partners," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 619-628, November.
    4. , & ,, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, vol. 1(2), pages 233-273, June.
    5. 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.
    6. Perez-Castrillo, David & Sotomayor, Marilda, 2002. "A Simple Selling and Buying Procedure," Journal of Economic Theory, Elsevier, vol. 103(2), pages 461-474, April.
    7. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    8. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    9. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    10. Sotomayor, Marilda, 1999. "Three remarks on the many-to-many stable matching problem," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 55-70, July.
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    Citations

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    Cited by:

    1. Yukihiko Funaki & Harold Houba & Evgenia Motchenkova, 2020. "Market power in bilateral oligopoly markets with non-expandable infrastructures," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 525-546, June.
    2. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    3. 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.
    4. 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.
    5. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    6. 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).
    7. Eric Bahel & Christian Trudeau, 2018. "Stable cost sharing in production allocation games," Review of Economic Design, Springer;Society for Economic Design, vol. 22(1), pages 25-53, June.
    8. repec:spa:wpaper:2013wpecon02 is not listed on IDEAS
    9. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.

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    More about this item

    Keywords

    matching; assignment; stability; lattice structure;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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