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Axioms of invariance for TU-games

Author

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  • Béal, Sylvain
  • Rémila, Eric
  • Solal, Philippe

Abstract

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

  • Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2012. "Axioms of invariance for TU-games," MPRA Paper 41530, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41530
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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. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Characterization of the Average Tree solution and its kernel," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 159-165.
    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. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    5. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    6. Pérez-Castrillo, David & Sun, Chaoran, 2021. "Value-free reductions," Games and Economic Behavior, Elsevier, vol. 130(C), pages 543-568.
    7. Macho-Stadler, Inés & Pérez-Castrillo, David & Wettstein, David, 2018. "Values for environments with externalities – The average approach," Games and Economic Behavior, Elsevier, vol. 108(C), pages 49-64.
    8. Sylvain Béal & Eric Rémila & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Theory and Decision, Springer, vol. 86(1), pages 95-106, February.
    9. Sylvain Ferrières, 2017. "Nullified equal loss property and equal division values," Theory and Decision, Springer, vol. 83(3), pages 385-406, October.
    10. 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.
    11. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.

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    More about this item

    Keywords

    uniform addition invariance ; uniform transfer invariance ; Shapley value ; equal division rule ; equal surplus division rule ; Banzhaf value;
    All these keywords.

    JEL classification:

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

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