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A Decomposition of the Space of TU-games Using Addition and Transfer Invariance

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Author Info

  • Sylvain Béal

    ()
    (CRESE, Université de Franche-Comté)

  • Eric Rémila

    ()
    (Gate Lyon Saint-Etienne, Université de Saint-etienne)

  • Philippe Solal

    ()
    (Gate Lyon Saint-Etienne, Université de Saint-etienne)

Abstract

In Béal et al. (2013) two new axioms of invariance, called Addition invariance and Transfer invariance respectively, are introduced to design allocation rules for TU-games. Here, we derive direct sum decompositions of the linear space of TU-games by using the TU-games selected to construct the operations of Addition and Transfer. These decompositions allow us to recover previous characterization results obtained by Béal et al. (2013), to provide new characterizations of well-known (class of) of allocation rules and also to design new allocation rules.

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File URL: http://crese.univ-fcomte.fr/WP-2013-08.pdf
File Function: First version, 2013
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Bibliographic Info

Paper provided by CRESE in its series Working Papers with number 2013-08.

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Length: 18 pages
Date of creation: Oct 2013
Date of revision:
Handle: RePEc:crb:wpaper:2013-08

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Keywords: addition invariance; transfer invariance; direct-sum decomposition; allocation rules;

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References

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  1. Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2007. "The consensus value: A new solution concept for cooperative games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-195202, Tilburg University.
  2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Axioms of invariance for TU-games," MPRA Paper 41530, University Library of Munich, Germany.
  3. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, vol. 23(1), pages 43-48.
  4. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
  5. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
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