IDEAS home Printed from https://ideas.repec.org/p/bge/wpaper/153.html
   My bibliography  Save this paper

Bargained stable allocations in assignment markets

Author

Listed:
  • Marina Núñez
  • Carles Rafels

Abstract

For each assignment market, an associated bargaining problem is defined and some bargaining solutions to this problem are analyzed. For a particular choice of the disagreement point, the Nash solution and the Kalai-Smorodinsky solution coincide and give the midpoint between the buyers-optimal core allocation and the sellers-optimal core allocation, and thus they belong to the core. Moreover, under the assumption that all agents in the market are active, the subset of core allocations that can be obtained as a Kalai- Smorodinsky solution, from some suitable disagreement point, is characterized as the set of stable allocations where each agent is paid at least half of his maximum core payoff. All allocations in this last set can also be obtained by a negotiation procedure µa la Nash.

Suggested Citation

  • Marina Núñez & Carles Rafels, 2004. "Bargained stable allocations in assignment markets," Working Papers 153, Barcelona School of Economics.
  • Handle: RePEc:bge:wpaper:153
    as

    Download full text from publisher

    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/153.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dagan, Nir & Volij, Oscar, 1993. "The bankruptcy problem: a cooperative bargaining approach," Mathematical Social Sciences, Elsevier, vol. 26(3), pages 287-297, November.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    4. Rochford, Sharon C., 1984. "Symmetrically pairwise-bargained allocations in an assignment market," Journal of Economic Theory, Elsevier, vol. 34(2), pages 262-281, December.
    5. Crawford, Vincent P & Rochford, Sharon C, 1986. "Bargaining and Competition in Matching Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(2), pages 329-348, June.
    6. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 413-420.
    7. Carmen Herrero, 1997. "Endogenous reference points and the adjusted proportional solution for bargaining problems with claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 113-119.
    8. Moldovanu, B, 1990. "Stable Bargained Equilibria for Assignment Games without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 171-190.
    9. Leonard, Herman B, 1983. "Elicitation of Honest Preferences for the Assignment of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 91(3), pages 461-479, June.
    10. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    12. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    13. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    14. Bennett, Elaine, 1988. "Consistent bargaining conjectures in marriage and matching," Journal of Economic Theory, Elsevier, vol. 45(2), pages 392-407, August.
    15. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marina Núñez & Carles Rafels, 2008. "A Cooperative Bargaining Approach to the Assignment Market," Group Decision and Negotiation, Springer, vol. 17(6), pages 553-563, November.
    2. José-Manuel Giménez-Gómez & António Osório & Josep E. Peris, 2015. "From Bargaining Solutions to Claims Rules: A Proportional Approach," Games, MDPI, vol. 6(1), pages 1-7, March.
    3. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    4. Trudeau, Christian, 2018. "From the bankruptcy problem and its Concede-and-Divide solution to the assignment problem and its Fair Division solution," Games and Economic Behavior, Elsevier, vol. 108(C), pages 225-238.
    5. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    6. Serrano, Roberto, 1997. "Reinterpreting the Kernel," Journal of Economic Theory, Elsevier, vol. 77(1), pages 58-80, November.
    7. Marco Mariotti, 2003. "Even Allocations For Generalised Rationing Problems," Working Papers. Serie AD 2003-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Mumcu, Ayse & Saglam, Ismail, 2006. "Marriage and Divorce in a Model of Matching," MPRA Paper 1907, University Library of Munich, Germany.
    9. Geoffroy de Clippel, 2009. "Axiomatic Bargaining on Economic Enviornments with Lott," Working Papers 2009-5, Brown University, Department of Economics.
    10. Fabio Galeotti & Maria Montero & Anders Poulsen, 2022. "The Attraction and Compromise Effects in Bargaining: Experimental Evidence," Management Science, INFORMS, vol. 68(4), pages 2987-3007, April.
    11. Subrato Banerjee, 2020. "Effect of reduced opportunities on bargaining outcomes: an experiment with status asymmetries," Theory and Decision, Springer, vol. 89(3), pages 313-346, October.
    12. Lombardi, Michele & Yoshihara, Naoki, 2010. "Alternative characterizations of the proportional solution for nonconvex bargaining problems with claims," Economics Letters, Elsevier, vol. 108(2), pages 229-232, August.
    13. Jaume García-Segarra & Miguel Ginés-Vilar, 2019. "Stagnation proofness in n-agent bargaining problems," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 215-224, March.
    14. Dagan, Nir & Serrano, Roberto, 1998. "Invariance and randomness in the Nash program for coalitional games," Economics Letters, Elsevier, vol. 58(1), pages 43-49, January.
    15. Roberto Serrano, 2007. "Bargaining," Working Papers 2007-06, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    16. Robert A. Pollak, 2019. "How Bargaining in Marriage Drives Marriage Market Equilibrium," Journal of Labor Economics, University of Chicago Press, vol. 37(1), pages 297-321.
    17. Giuseppe Liddo & Michele G. Giuranno, 2020. "The political economy of municipal consortia and municipal mergers," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 37(1), pages 105-135, April.
    18. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.
    19. Dominik Karos, 2015. "Stable partitions for games with non-transferable utilities and externalities," Economics Series Working Papers 741, University of Oxford, Department of Economics.
    20. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.

    More about this item

    Keywords

    assignment game; core; bargaining problem; Nash solution; Kalai-Smorodinsky solution;
    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

    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:bge:wpaper:153. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Bruno Guallar (email available below). General contact details of provider: https://edirc.repec.org/data/bargses.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.