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Symmetrically multilateral-bargained allocations in multi-sided assignment markets

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  • Oriol Tejada
  • Carles Rafels

Abstract

We extend Rochfords (1983) notion of symmetrically pairwise-bargained equilibrium to assignment games with more than two sides. A symmetrically multilateral-bargained (SMB) allocation is a core allocation such that any agent is in equilibrium with respect to a negotiation process among all agents based on what every agent could receive -and use as a threat- in her preferred alternative matching to the optimal matching that is formed. We prove that, for balanced multi-sided assignment games, the set of SMB is always nonempty and that, unlike the two-sided case, it does not coincide in general with the kernel (Davis and Maschler, 1965). We also give an answer to an open question formulated by Rochford (1983) by introducing a kernel-based set that, together with the core, characterizes the set of SMB.
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  • Oriol Tejada & Carles Rafels, 2010. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 249-258, March.
    • Handle: RePEc:spr:jogath:v:39:y:2010:i:1:p:249-258
    DOI: 10.1007/s00182-009-0204-3
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    References listed on IDEAS

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    1. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
    2. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 301-303.
    4. Daniel Granot & Frieda Granot, 1992. "On Some Network Flow Games," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 792-841, November.
    5. Kaneko, Mamoru & Wooders, Myrna Holtz, 1982. "Cores of partitioning games," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 313-327, December.
    6. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    7. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    8. Oriol Tejada & Carles Rafels, 2009. "Competitive prices of homogeneous goods in multilateral markets," Working Papers 370, Barcelona School of Economics.
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    Cited by:

    1. Elena Iñarra & Roberto Serrano & Ken-Ichi Shimomura, 2020. "The Nucleolus, the Kernel, and the Bargaining Set: An Update," Revue économique, Presses de Sciences-Po, vol. 71(2), pages 225-266.
    2. O. Tejada and M. Alvarez-Mozos, 2012. "Vertical Syndication-Proof Competitive Prices in Multilateral Markets," Working Papers in Economics 283, Universitat de Barcelona. Espai de Recerca en Economia.
    3. Oriol Tejada, 2013. "Complements and Substitutes in Generalized Multisided Assignment Economies," CER-ETH Economics working paper series 13/180, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    4. Oriol Tejada & Marina Núñez, 2012. "The nucleolus and the core-center of multi-sided Böhm-Bawerk assignment markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(2), pages 199-220, April.
    5. Oriol Tejada, 2013. "Analysis of the core of multisided Böhm-Bawerk assignment markets," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 189-205, April.

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    More about this item

    Keywords

    Cooperative games; Core; kernel; Bargaining;
    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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