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A note on the monotonicity and superadditivity of TU cooperative games

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  • Jean-François Caulier

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this note we make a comparison between the class of monotonic TU cooperative games and the class of superadditive TU cooperative games. We first provide the equivalence between a weakening of the class of su- peradditive TU games and zero-monotonic TU games. Then, we show that zero-monotonic TU games and monotonic TU games are different classes. Finally, we show under which restrictions the classes of superadditive and monotonic TU games can be related.

Suggested Citation

  • Jean-François Caulier, 2009. "A note on the monotonicity and superadditivity of TU cooperative games," Working Papers hal-00633612, HAL.
    • Handle: RePEc:hal:wpaper:hal-00633612
    Note: View the original document on HAL open archive server: https://hal.science/hal-00633612
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    References listed on IDEAS

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    1. Jean-Yves Jaffray & Philippe Mongin, 2003. "Constrained egalitarianism in a simple redistributive model," Theory and Decision, Springer, vol. 54(1), pages 33-56, February.
    2. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    3. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, March.
    4. Laruelle,Annick & Valenciano,Federico, 2011. "Voting and Collective Decision-Making," Cambridge Books, Cambridge University Press, number 9780521182638.
    5. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    6. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    7. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
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