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Axioms of invariance for TU-games

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

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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File URL: http://mpra.ub.uni-muenchen.de/41530/1/MPRA_paper_41530.pdf
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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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  1. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
  2. Samuelson, Paul A & Swamy, S, 1974. "Invariant Economic Index Numbers and Canonical Duality: Survey and Synthesis," American Economic Review, American Economic Association, vol. 64(4), pages 566-93, September.
  3. 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.
  4. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
  5. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
  6. 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.
  7. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
  8. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer, vol. 39(3), pages 467-482, July.
  9. Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2004. "The Consensus Value : A New Solution Concept for Cooperative Games," Discussion Paper 2004-50, Tilburg University, Center for Economic Research.
  10. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58, pages 328.
  11. Willig, Robert D, 1977. "Risk Invariance and Ordinally Additive Utility Functions," Econometrica, Econometric Society, vol. 45(3), pages 621-40, April.
  12. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
  13. Gordon Kemp, 2000. "Invariance and the Wald Test," Economics Discussion Papers 526, University of Essex, Department of Economics.
  14. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer, vol. 30(2), pages 279-289.
  15. Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2007. "The consensus value : A new solution concept for cooperative games," Other publications TiSEM 6cd44a12-a909-47f8-8d85-e, Tilburg University, School of Economics and Management.
  16. 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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