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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. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    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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