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On (Non-) Monotonicity of Cooperative Solutions

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Author Info

  • 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.

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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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Bibliographic Info

Paper provided by Kyiv School of Economics in its series Discussion Papers with number 13.

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Date of creation: Jan 2009
Date of revision: Oct 2009
Handle: RePEc:kse:dpaper:13

Note: Published in International Journal of Game Theory 39, 171-175 (2010)
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Related research

Keywords: Cooperative games; aggregate monotonicity; axiomatic solution; core; Shapley value; nucleolus;

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References

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  1. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer, vol. 32(2), pages 189-204, December.
  2. 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.
  3. Toru Hokari, 2000. "note: The nucleolus is not aggregate-monotonic on the domain of convex games," International Journal of Game Theory, Springer, vol. 29(1), pages 133-137.
  4. Arin, J. & Feltkamp, V., 1994. "The nucleolus and kernel of veto-rich transferable utility games," Discussion Paper 1994-40, Tilburg University, Center for Economic Research.
  5. Potters, J.A.M. & Poos, R. & Tijs, S.H. & Muto, S., 1989. "Clan games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154241, Tilburg University.
  6. Moulin, Herve & Thomson, William, 1988. "Can everyone benefit from growth? : Two difficulties," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 339-345, September.
  7. Potters, Jos & Poos, Rene & Tijs, Stef & Muto, Shigeo, 1989. "Clan games," Games and Economic Behavior, Elsevier, vol. 1(3), pages 275-293, September.
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Cited by:
  1. J. Arin, 2013. "Monotonic core solutions: beyond Young’s theorem," International Journal of Game Theory, Springer, vol. 42(2), pages 325-337, May.

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