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On (non-) monotonicity of cooperative solutions

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  • Yair Tauman
  • Andriy Zapechelnyuk

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.
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  • Yair Tauman & Andriy Zapechelnyuk, 2010. "On (non-) monotonicity of cooperative solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 171-175, March.
    • Handle: RePEc:spr:jogath:v:39:y:2010:i:1:p:171-175
    DOI: 10.1007/s00182-009-0196-z
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    5. 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.
    6. 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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    9. 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.
    10. 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.
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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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    More about this item

    Keywords

    Cooperative games; Aggregate monotonicity; Axiomatic solution; Core; Shapley value; Nucleolus; C71; C78;
    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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