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Preserving or removing special players: what keeps your payoff unchanged in TU-games?

Author

Listed:
  • Sylvain Béal

    () (CRESE, Université de Franche-Comté)

  • Eric Rémila

    () (Gate Lyon Saint-Etienne, Université de Saint-etienne)

  • Philippe Solal

    () (Gate Lyon Saint-Etienne, Université de Saint-etienne)

Abstract

If a player is removed from a game, what keeps the payoff of the remaining players unchanged? Is it the removal of a special player or its presence among the remaining players? This article answers this question in a complement study to Kamijo and Kongo (2012). We introduce axioms of invariance from player deletion in presence of a special player. In particular, if the special player is a nullifying player (resp. dummifying player), then the equal division value (resp. equal surplus division value) is characterized by the associated axiom of invariance plus efficiency and balanced cycle contributions. There is no type of special player from such a combination of axioms that characterizes the Shapley value.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Preserving or removing special players: what keeps your payoff unchanged in TU-games?," Working Papers 2013-09, CRESE.
  • Handle: RePEc:crb:wpaper:2013-09
    as

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    File URL: http://crese.univ-fcomte.fr/WP-2013-09.pdf
    File Function: First version, 2013
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Youngsub Chun & Boram Park, 2012. "Population solidarity, population fair-ranking, and the egalitarian value," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(2), pages 255-270, May.
    5. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
    6. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    7. Radzik, Tadeusz, 2012. "A new look at the role of players’ weights in the weighted Shapley value," European Journal of Operational Research, Elsevier, vol. 223(2), pages 407-416.
    8. 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.
    9. 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.
    10. Casajus, André & Hüttner, Frank, 2012. "Nullifying vs. dummifying players or nullified vs. dummified players: The difference between the equal division value and the equal surplus division value," Working Papers 110, University of Leipzig, Faculty of Economics and Management Science.
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    Cited by:

    1. repec:kap:theord:v:83:y:2017:i:1:d:10.1007_s11238-017-9586-z is not listed on IDEAS
    2. 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.
    3. Sylvain Béal & Eric Rémila & Philippe Solal, 2017. "Axiomatization and implementation of a class of solidarity values for TU-games," Theory and Decision, Springer, vol. 83(1), pages 61-94, June.
    4. Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.
    5. repec:kap:theord:v:83:y:2017:i:3:d:10.1007_s11238-017-9604-1 is not listed on IDEAS
    6. Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.

    More about this item

    Keywords

    weighted division values; equal division; weighted surplus division values; equal surplus division; Shapley value; null player; nullifying player; dummifying player; invariance from player deletion in presence of a special player;

    JEL classification:

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

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