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One-seller assignment markets with multiunit demands

Author

Listed:
  • Francisco Robles

    (Facultat d'Economia i Empresa; Universitat de Barcelona (UB))

  • Marina Núñez

    (Facultat d'Economia i Empresa; Universitat de Barcelona (UB))

Abstract

We consider one-seller assignment markets with multi-unit demands and prove that the associated game is buyers-submodular. Therefore the core is non-empty and it has a lattice structure which contains the allocation where every buyer receives his marginal contribution. We prove that in this kind of market, every pairwise-stable outcome is associated to a competitive equilibrium and vice versa. We study conditions under which the buyers-optimal and the seller-optimal core allocations are competitive equilibrium payoff vectors. Moreover, we characterize the markets for which the core coincidences with the set of competitive equilibria payoff vectors. When agents behave strategically, we introduce a procedure that implements the buyers-optimal core allocation as the unique subgame perfect Nash equilibrium outcome.

Suggested Citation

  • 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.
    • Handle: RePEc:ewp:wpaper:316web
    as

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    References listed on IDEAS

    as
    1. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    2. Perez-Castrillo, David & Sotomayor, Marilda, 2002. "A Simple Selling and Buying Procedure," Journal of Economic Theory, Elsevier, vol. 103(2), pages 461-474, April.
    3. 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.
    4. William Vickrey, 1961. "Counterspeculation, Auctions, And Competitive Sealed Tenders," Journal of Finance, American Finance Association, vol. 16(1), pages 8-37, March.
    5. Tauman, Yair & Urbano, Amparo & Watanabe, Junichi, 1997. "A Model of Multiproduct Price Competition," Journal of Economic Theory, Elsevier, vol. 77(2), pages 377-401, December.
    6. 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.
    7. Marilda Sotomayor, 1992. "The Multiple Partners Game," Palgrave Macmillan Books, in: Mukul Majumdar (ed.), Equilibrium and Dynamics, chapter 17, pages 322-354, Palgrave Macmillan.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Many-to-many assignment markets; Core; Pairwise-stability; Competitive equilibrium.;
    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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