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Axioms of Invariance for TU-games

Author

Listed:
  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Éric Rémila

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'Analyse et de Théorie Economique Lyon - Saint-Etienne - ENS de Lyon - École normale supérieure de Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Sylvain Béal & Éric Rémila & Philippe Solal, 2015. "Axioms of Invariance for TU-games," Post-Print halshs-01096552, HAL.
    • Handle: RePEc:hal:journl:halshs-01096552
    DOI: 10.1007/s00182-014-0458-2
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    References listed on IDEAS

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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.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 28(4), pages 685-703, June.
    4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    5. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    6. Kemp, Gordon C. R., 2001. "Invariance and the Wald test," Journal of Econometrics, Elsevier, vol. 104(2), pages 209-217, September.
    7. 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.
    8. Carl Futia, 2010. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Levine's Working Paper Archive 497, David K. Levine.
    9. André Casajus, 2011. "Differential marginality, van den Brink fairness, and the Shapley value," Theory and Decision, Springer, vol. 71(2), pages 163-174, August.
    10. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    11. Gérard Hamiache, 2001. "Associated consistency and Shapley value," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 279-289.
    12. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    13. 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 566-593, September.
    14. Willig, Robert D, 1977. "Risk Invariance and Ordinally Additive Utility Functions," Econometrica, Econometric Society, vol. 45(3), pages 621-640, April.
    15. Chameni Nembua, C., 2012. "Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation," Games and Economic Behavior, Elsevier, vol. 74(1), pages 431-433.
    16. Theo Driessen, 2010. "Associated consistency and values for TU games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 467-482, July.
    17. Kenneth J. Arrow, 1950. "A Difficulty in the Concept of Social Welfare," Journal of Political Economy, University of Chicago Press, vol. 58(4), pages 328-328.
    18. Marcin Malawski, 2002. "Equal treatment, symmetry and Banzhaf value axiomatizations," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 47-67.
    19. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 43-48.
    20. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    21. 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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    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

    Game Theory;

    JEL classification:

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

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