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Effects of Players’ Nullification and Equal (Surplus) Division Values

Author

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  • Takumi Kongo

    (Faculty of Economics, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan)

Abstract

We provide axiomatic characterizations of the solutions of transferable utility (TU) games on the fixed player set, where at least three players exist. We introduce two axioms on players’ nullification. One axiom requires that the difference between the effect of a player’s nullification on the nullified player and on the others is relatively constant if all but one players are null players. Another axiom requires that a player’s nullification affects equally all of the other players. These two axioms characterize the set of all affine combinations of the equal surplus division and equal division values, together with the two basic axioms of efficiency and null game. By replacing the first axiom on players’ nullification with appropriate monotonicity axioms, we narrow down the solutions to the set of all convex combinations of the two values, or to each of the two values.

Suggested Citation

  • Takumi Kongo, 2018. "Effects of Players’ Nullification and Equal (Surplus) Division Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-14, March.
    • Handle: RePEc:wsi:igtrxx:v:20:y:2018:i:01:n:s0219198917500293
    DOI: 10.1142/S0219198917500293
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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. René Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2016. "Consistency, population solidarity, and egalitarian solutions for TU-games," Theory and Decision, Springer, vol. 81(3), pages 427-447, 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. 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.
    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. 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.
    7. 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.
    8. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Preserving or removing special players: What keeps your payoff unchanged in TU-games?," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 23-31.
    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. 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.
    11. Sylvain Béal & Marc Deschamps & Philippe Solal, 2016. "Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(6), pages 992-1004, December.
    12. Yoshio Kamijo & Takumi Kongo, 2015. "Properties based on relative contributions for cooperative games with transferable utilities," Theory and Decision, Springer, vol. 78(1), pages 77-87, January.
    13. René Brink & Yukihiko Funaki & Yuan Ju, 2013. "Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 693-714, March.
    14. 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.
    15. 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.
    16. Rene van den Brink, 2009. "Efficiency and Collusion Neutrality of Solutions for Cooperative TU-Games," Tinbergen Institute Discussion Papers 09-065/1, Tinbergen Institute.
    17. Sylvain Ferrières, 2017. "Nullified equal loss property and equal division values," Theory and Decision, Springer, vol. 83(3), pages 385-406, October.
    18. Sylvain Ferrières, 2016. "Nullified equal loss property and equal division values," Working Papers 2016-06, CRESE.
    19. Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.
    20. Neyman, Abraham, 1989. "Uniqueness of the Shapley value," Games and Economic Behavior, Elsevier, vol. 1(1), pages 116-118, March.
    21. Koji Yokote & Yukihiko Funaki, 2017. "Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 171-203, June.
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    Cited by:

    1. 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.
    2. Zou, Zhengxing & van den Brink, René, 2020. "Equal loss under separatorization and egalitarian values," Economics Letters, Elsevier, vol. 194(C).
    3. Xun-Feng Hu & Gen-Jiu Xu & Deng-Feng Li, 2019. "The Egalitarian Efficient Extension of the Aumann–Drèze Value," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 1033-1052, June.
    4. Xun-Feng Hu & Deng-Feng Li, 2021. "The Equal Surplus Division Value for Cooperative Games with a Level Structure," Group Decision and Negotiation, Springer, vol. 30(6), pages 1315-1341, December.
    5. Takumi Kongo, 2020. "Similarities in axiomatizations: equal surplus division value and first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 199-213, December.
    6. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2019. "Relationally equal treatment of equals and affine combinations of values for TU games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 197-212, August.
    7. Kongo, Takumi, 2019. "Players’ nullification and the weighted (surplus) division values," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    8. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2021. "Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values," Theory and Decision, Springer, vol. 91(1), pages 81-98, July.

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    More about this item

    Keywords

    TU game; axiomatization; equal division value; equal surplus division value; nullification;
    All these keywords.

    JEL classification:

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

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