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Sharing the Surplus and Proportional Values

Author

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  • Zhengxing Zou

    (Vrije Universiteit Amsterdam)

  • Rene van den Brink

    (Vrije Universiteit Amsterdam)

Abstract

We introduce a family of proportional surplus division values for TU-games. Each value ï¬ rst assigns to each player a compromise between his stand-alone worth and the average stand-alone worths over all players, and then allocates the remaining worth among the players in proportion to their stand-alone worths. This family contains the proportional division value and the new egalitarian proportional surplus division value as two special cases. We provide characterizations for this family of values, as well as for each single value in this family.

Suggested Citation

  • Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20200014
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    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. 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.
    3. 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.
    4. 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.
    5. Tijs, S.H. & Driessen, T.S.H., 1986. "Game theory and cost allocation problems," Other publications TiSEM 376c24c5-c95d-4d29-96b6-4, Tilburg University, School of Economics and Management.
    6. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    7. 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.
    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. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Hao Sun, 2019. "Procedural and optimization implementation of the weighted ENSC value," Theory and Decision, Springer, vol. 87(2), pages 171-182, September.
    10. 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.
    11. 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.
    12. 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.
    13. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    14. 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.
    15. van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.
    16. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, April.
    17. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    18. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    19. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    20. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    21. Genjiu Xu & Han Dai & Haobin Shi, 2015. "Axiomatizations and a Noncooperative Interpretation of the α-CIS Value," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-15.
    22. Pedro Calleja & Francesc Llerena, 2019. "Path monotonicity, consistency and axiomatizations of some weighted solutions," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 287-310, March.
    23. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
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    Cited by:

    1. Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    2. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2022. "Lexicographic solutions for coalitional rankings based on individual and collective performances," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. Zou, Zhengxing & van den Brink, René, 2020. "Equal loss under separatorization and egalitarian values," Economics Letters, Elsevier, vol. 194(C).
    4. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).

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    More about this item

    Keywords

    Cooperative game; proportional value; surplus sharing; axiomatization; balanced contributions;
    All these keywords.

    JEL classification:

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

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