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On (Non-) Monotonicity of Cooperative Solutions

Author

Listed:
  • Yair Tauman

    (Tel Aviv University and Stony Brook University)

  • Andriy Zapechelnyuk

    (University of Bonn and Kyiv School of Economics)

Abstract

Aggregate monotonicity of cooperative solutions is widely accepted as a desirable property, and examples where certain solution concepts (such as the nucleolus) violate this property are scarce and have no economic interpretation. We provide an example of a simple four-player game that points out at a class of economic contexts where aggregate monotonicity is not appealing.

Suggested Citation

  • Yair Tauman & Andriy Zapechelnyuk, 2009. "On (Non-) Monotonicity of Cooperative Solutions," Discussion Papers 13, Kyiv School of Economics, revised Oct 2009.
    • Handle: RePEc:kse:dpaper:13
    Note: Published in International Journal of Game Theory 39, 171-175 (2010)
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    File URL: http://repec.kse.org.ua/pdf/KSE_dp13.pdf
    File Function: Revised version, October 2009
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    References listed on IDEAS

    as
    1. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
    2. Bezalel Peleg & Peter Sudholter, 2004. "Bargaining Sets of Voting Games," Discussion Paper Series dp376, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    4. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 133-137.
    5. 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.
    6. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Other publications TiSEM 1855e4e3-7392-4ef0-a073-8, Tilburg University, School of Economics and Management.
    7. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 189-204, December.
    8. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    9. Vincent Feltkamp & Javier Arin, 1997. "The Nucleolus and Kernel of Veto-Rich Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 61-73.
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    Citations

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    Cited by:

    1. J. Arin, 2013. "Monotonic core solutions: beyond Young’s theorem," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 325-337, May.
    2. A. Estévez-Fernández & P. Borm & M. G. Fiestras-Janeiro & M. A. Mosquera & E. Sánchez-Rodríguez, 2017. "On the 1-nucleolus," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 309-329, October.
      • Estévez-Fernández , M.A. & Borm, Peter & Fiestras, & Mosquera, & Sanchez,, 2017. "On the 1-nucleolus," Other publications TiSEM a8ce6687-c87a-4131-98f7-3, Tilburg University, School of Economics and Management.
    3. Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2021. "Considerations on the aggregate monotonicity of the nucleolus and the core-center," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(2), pages 291-325, April.

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    Keywords

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    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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