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Axiomatic characterizations under players nullification

Author

Listed:
  • Sylvain Béal

    (CRESE EA3190, Univ. Bourgogne Franche-Comté)

  • Sylvain Ferrières

    (CRESE EA3190, Univ. Bourgogne Franche-Comté, Chair of Economics and Information Systems, HHL Leipzig Graduate School of Management)

  • Eric Rémila

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

Abstract

Many axiomatic characterizations of values for cooperative games invoke axioms which evaluate the consequences of removing an arbitrary player. Balanced contributions (Myerson, 1980) and balanced cycle contributions (Kamijo and Kongo, 2010) are two well-known examples of such axioms. We revisit these characterizations by nullifying a player instead of deleting her/him from a game. The nullification (Béal et al., 2014) of a player is obtained by transforming a game into a new one in which this player is a null player, i.e. the worth of the coalitions containing this player is now identical to that of the same coalition without this player. The degree with which our results are close to the original results in the literature is connected to the fact that the targeted value satisfies the null player out axiom (Derks and Haller, 1999).

Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Eric Rémila & Philippe Solal, 2015. "Axiomatic characterizations under players nullification," Working Papers 2015-06, CRESE.
  • Handle: RePEc:crb:wpaper:2015-06
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    References listed on IDEAS

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    1. Dehez, Pierre & Ferey, Samuel, 2013. "How to share joint liability: A cooperative game approach," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 44-50.
    2. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    3. André Casajus, 2014. "Collusion, quarrel, and the Banzhaf value," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 1-11, February.
    4. Marc Fleurbaey & François Maniquet, 2006. "Compensation and responsibility," Working Papers halshs-00121367, HAL.
    5. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    6. Gómez-Rúa, María & Vidal-Puga, Juan, 2010. "The axiomatic approach to three values in games with coalition structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 795-806, December.
    7. Ehud Kalai & Eitan Zemel, 1982. "Totally Balanced Games and Games of Flow," Mathematics of Operations Research, INFORMS, vol. 7(3), pages 476-478, August.
    8. Sylvain Béal & André Casajus & Frank Huettner & Eric Rémila & Philippe Solal, 2016. "Characterizations of weighted and equal division values," Theory and Decision, Springer, vol. 80(4), pages 649-667, April.
    9. Rodica Brânzei & Vito Fragnelli & Stef Tijs, 2002. "Tree-connected peer group situations and peer group games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(1), pages 93-106, March.
    10. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    11. Jean J. M. Derks & Hans H. Haller, 1999. "Null Players Out? Linear Values For Games With Variable Supports," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 301-314.
    12. Thomson, William, 2012. "On The Axiomatics Of Resource Allocation: Interpreting The Consistency Principle," Economics and Philosophy, Cambridge University Press, vol. 28(3), pages 385-421, November.
    13. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    14. Yevgenia Apartsin & Ron Holzman, 2003. "The core and the bargaining set in glove-market games," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(2), pages 189-204, December.
    15. Béal, Sylvain & Casajus, André & Huettner, Frank & Rémila, Eric & Solal, Philippe, 2014. "Solidarity within a fixed community," Economics Letters, Elsevier, vol. 125(3), pages 440-443.
    16. 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.
    17. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 563-571, October.
    18. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    19. Sylvain Béal & Marc Deschamps & Philippe Solal, 2014. "Balanced collective contributions, the equal allocation of non-separable costs and application to data sharing games," Working Papers hal-01377926, HAL.
    20. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
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    Cited by:

    1. Kongo, Takumi, 2018. "Balanced contributions based on indirect claims and the Shapley value," Economics Letters, Elsevier, vol. 167(C), pages 48-50.
    2. de Clippel, Geoffroy, 2018. "Membership separability: A new axiomatization of the Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 125-129.
    3. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    4. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    5. Ricardo Mart'inez & Joaqu'in S'anchez-Soriano, 2023. "Order preservation with dummies in the musseum pass problem," Papers 2307.00622, arXiv.org.
    6. Zhang, Li & Xu, Genjiu & Sun, Hao & Li, Wenzhong, 2023. "Players’ dummification and the dummified egalitarian non-separable contribution value," Economics Letters, Elsevier, vol. 226(C).
    7. Takaaki Abe & Satoshi Nakada, 2023. "Potentials and solutions of cooperative games with a fixed player set," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 757-774, September.
    8. C. Manuel & E. Ortega & M. del Pozo, 2023. "Marginality and the position value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 459-474, July.
    9. Zou, Zhengxing & van den Brink, René, 2020. "Equal loss under separatorization and egalitarian values," Economics Letters, Elsevier, vol. 194(C).
    10. Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "Social solidarity with dummies in the museum pass problem," ThE Papers 21/11, Department of Economic Theory and Economic History of the University of Granada..
    11. Yokote, Koji & Kongo, Takumi & Funaki, Yukihiko, 2018. "The balanced contributions property for equal contributors," Games and Economic Behavior, Elsevier, vol. 108(C), pages 113-124.
    12. Sylvain Ferrières, 2017. "Nullified equal loss property and equal division values," Theory and Decision, Springer, vol. 83(3), pages 385-406, October.
    13. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    14. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    15. Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.
    16. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.

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    More about this item

    Keywords

    Player nullification; balanced contributions; Shapley value; equal allocation of non-separable costs; potential.;
    All these keywords.

    JEL classification:

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

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