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A Characterization of Egalitarian and Proportional Sharing Principles: An Efficient Extension Operator Approach

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  • Yukihiko Funaki
  • Yukio Koriyama
  • Satoshi Nakada

Abstract

Some well-known solutions for cooperative games with transferable utility (TU-games), such as the Banzhaf value, the Myerson value, and the Aumann-Dreze value, fail to satisfy efficiency. Despite their desirable normative properties, this inefficiency motivates the search for a systematic method to restore efficiency while preserving their underlying normative structure. This paper proposes an efficient extension operator as a general approach to restore efficiency by extending any underlying solution to an efficient one. We consider novel axioms for those operators and characterize the egalitarian surplus sharing method and the proportional sharing method in a unified manner. As applications, we demonstrate the generality of our method by developing an efficient-fair extension of solutions for TU games with communication networks, as well as a variant for TU games with coalition structures.

Suggested Citation

  • Yukihiko Funaki & Yukio Koriyama & Satoshi Nakada, 2025. "A Characterization of Egalitarian and Proportional Sharing Principles: An Efficient Extension Operator Approach," Papers 2510.24388, arXiv.org, revised Aug 2026.
    • Handle: RePEc:arx:papers:2510.24388
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    References listed on IDEAS

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    1. Dogan, Battal & Ehlers, Lars, 2021. "Minimally unstable Pareto improvements over deferred acceptance," Theoretical Economics, Econometric Society, vol. 16(4), November.
    2. 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.
    3. van den Brink, René & Khmelnitskaya, Anna & van der Laan, Gerard, 2012. "An efficient and fair solution for communication graph games," Economics Letters, Elsevier, vol. 117(3), pages 786-789.
    4. 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.
    5. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    6. Zou, Zhengxing & Tan, Zhibin, 2023. "Axiomatizations of convex compromise rules for redistribution of non-negative income," Economics Letters, Elsevier, vol. 229(C).
    7. 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.
    8. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
    9. 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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