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Axioms of invariance for TU-games

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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.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41530.

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Date of creation: 24 Sep 2012
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Handle: RePEc:pra:mprapa:41530

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

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  1. Kamiya, Kazuya & Talman, Dolf, 2009. "Matching models with a conservation law: The existence and global structure of the set of stationary equilibria," Journal of Mathematical Economics, Elsevier, vol. 45(5-6), pages 397-413, May.
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  13. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
  14. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
  15. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
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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. Casajus, André, 2014. "The Shapley value without efficiency and additivity," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 1-4.

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