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

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Author Info

  • 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.

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File URL: http://crese.univ-fcomte.fr/WP-2013-09.pdf
File Function: First version, 2013
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Bibliographic Info

Paper provided by CRESE in its series Working Papers with number 2013-09.

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Length: 16 pages
Date of creation: Nov 2013
Date of revision:
Handle: RePEc:crb:wpaper:2013-09

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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;

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References

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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, vol. 28(4), pages 685-703, June.
  2. Casajus, André & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
  3. Yoshio Kamijo & Takumi Kongo, 2010. "Axiomatization of the Shapley value using the balanced cycle contributions property," International Journal of Game Theory, Springer, vol. 39(4), pages 563-571, October.
  4. 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.
  5. 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.
  6. Casajus, André & Hüttner, Frank, 2012. "Null players, solidarity, and the egalitarian Shapley values," Working Papers 113, University of Leipzig, Faculty of Economics and Management Science.
  7. Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, vol. 23(1), pages 43-48.
  8. Rene van den Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2012. "Consistency, Population Solidarity, and Egalitarian Solutions for TU-Games," Tinbergen Institute Discussion Papers 12-136/II, Tinbergen Institute.
  9. 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.
  10. Youngsub Chun & Boram Park, 2012. "Population solidarity, population fair-ranking, and the egalitarian value," International Journal of Game Theory, Springer, vol. 41(2), pages 255-270, May.
  11. 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.
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