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Axioms of invariance for TU-games

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  • Sylvain Béal
  • Eric Rémila
  • Philippe Solal

Abstract

We introduce new axioms for the class of all TU-games with a fixed but arbitrary player set. These axioms require either invariance of an allocation rule or invariance of the payoff assigned by an allocation rule to a specified player in two related TU-games. Combinations of these new axioms are used to characterize the Shapley value, the Equal Division rule, and the Equal Surplus Division rule. The classical axioms of Efficiency, Anonymity, Equal treatment of equals, Additivity and Linearity are not used. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:4:p:891-902
    DOI: 10.1007/s00182-014-0458-2
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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

    Addition invariance; Equal (Surplus) Division rule; Transfer invariance; Shapley value;
    All these keywords.

    JEL classification:

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

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