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Bargained stable allocations in assignment markets

Author

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  • 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 Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:153
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    References listed on IDEAS

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    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. 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.
    3. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    4. 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.
    5. Bennett, Elaine, 1988. "Consistent bargaining conjectures in marriage and matching," Journal of Economic Theory, Elsevier, vol. 45(2), pages 392-407, August.
    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. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    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. 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.
    10. 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.
    11. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    12. Rochford, Sharon C., 1984. "Symmetrically pairwise-bargained allocations in an assignment market," Journal of Economic Theory, Elsevier, vol. 34(2), pages 262-281, December.
    13. 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.
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    More about this item

    Keywords

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

    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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