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Axioms of Invariance for TU-games


  • 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)


We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set, which require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified subset of players in two related TU-games. Comparisons with other axioms are provided. These new axioms are used to characterize the Shapley value, the equal division rule, the equal surplus division rule and the Banzhaf value. The classical axioms of efficiency, anonymity, symmetry and additivity are not used.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2012. "Axioms of Invariance for TU-games," Working Papers 2012-01, CRESE.
  • Handle: RePEc:crb:wpaper:2012-01

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    References listed on IDEAS

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    Cited by:

    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "A Decomposition of the Space of TU-games Using Addition and Transfer Invariance," Working Papers 2013-08, CRESE.
    2. Koji Yokote, 2015. "Weak addition invariance and axiomatization of the weighted Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 275-293, May.
    3. Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    4. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    5. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.
    6. Ines Macho-Stadler & David Pérez-Castrillo & David Wettstein, 2016. "Values for Environments with Externalities - The Average Approach," CESifo Working Paper Series 6002, CESifo Group Munich.
    7. Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.
    8. repec:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9604-1 is not listed on IDEAS

    More about this item


    uniform addition invariance; uniform transfer invariance; Shapley value; equal division rule; equal surplus division rule; Banzhaf value;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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